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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <br/> for <font color="Olive" title="b4">E</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b1">S</font>  st <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">E</font> &amp; <font color="Olive" title="b2">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b4">E</font> &amp; <font color="Olive" title="b3">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b4">E</font> holds <br/><font color="Olive" title="b2">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Olive" title="b3">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b4">E</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> <br/> for <font color="Olive" title="b3">E</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font>  st <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b2">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">E</font> &amp; <font color="Olive" title="b1">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b3">E</font> &amp; <font color="Olive" title="b2">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b3">E</font> holds <br/><font color="Olive" title="b1">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Olive" title="b2">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b3">E</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">E</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font>  st <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Maroon" title="c3">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b1">E</font> &amp; <font color="Maroon" title="c4">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b1">E</font> holds <br/><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c4">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Olive" title="b1">E</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">E</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">E</font> &amp; <font color="Maroon" title="c3">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font> &amp; <font color="Maroon" title="c4">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font> implies <font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c4">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font> )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:50"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">E</font>
 <span class="kw">and </span><br/><a NAME="E2:50"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 <span class="kw">and </span><br/><a NAME="E3:50"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c4">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c4">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font></span><br/>

<a NAME="E4:50"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun6c.html#D2" title="MESFUN6C:def.2">MESFUN6C:def 2</a></span>;<br/>
<a NAME="E5:50"/><span class="lab"><font color="Green" title="E31">A5</font></span>: 
 <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c3">f</font> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="mesfun6c.html#D3" title="MESFUN6C:def.3">MESFUN6C:def 3</a></span>;<br/>
<a NAME="E6:50"/><span class="lab"><font color="Green" title="E32">A6</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun6c.html#D2" title="MESFUN6C:def.2">MESFUN6C:def 2</a></span>;<br/>
<a NAME="E7:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A7</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E4:50"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="valued_1.html#D4" title="VALUED_1:def.4">VALUED_1:def 4</a></span>;<br/>
<a NAME="E8:50"/><span class="lab"><font color="Green" title="E34">A8</font></span>: 
 <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c4">g</font> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="mesfun6c.html#D3" title="MESFUN6C:def.3">MESFUN6C:def 3</a></span>;<br/>
<a NAME="E9:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A9</font></span>: 
<span class="p1">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E5:50"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="txt" href="#E4:50"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="mesfun7c.html#T31" target="_self" title="MESFUN7C:th.31">Th31</a></span>;<br/>
<a NAME="E10:50"/><span class="lab"><font color="Green" title="E36">A10</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun6c.html#D1" title="MESFUN6C:def.1">MESFUN6C:def 1</a></span>;<br/>
<a NAME="E11:50"/><span class="lab"><font color="Green" title="E37">A11</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">g</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun6c.html#D1" title="MESFUN6C:def.1">MESFUN6C:def 1</a></span>;<br/>
<a NAME="E12:50"/><span class="lab"><font color="Green" title="E38">A12</font></span>: 
 <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c4">g</font> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:50"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="mesfun6c.html#D3" title="MESFUN6C:def.3">MESFUN6C:def 3</a></span>;<br/>
<a NAME="E13:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A13</font></span>: 
<span class="p1">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E5:50"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="txt" href="#E6:50"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="txt" href="#E11:50"><span class="lab"><font color="Green" title="E37">A11</font></span></a>, <a class="ref" href="mesfun7c.html#T31" target="_self" title="MESFUN7C:th.31">Th31</a></span>;<br/>
<a NAME="E14:50"/><span class="lab"><font color="Green" title="E40">A14</font></span>: 
 <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c3">f</font> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:50"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="ref" href="mesfun6c.html#D3" title="MESFUN6C:def.3">MESFUN6C:def 3</a></span>;<br/>
<a NAME="E15:50"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E8:50"><span class="lab"><font color="Green" title="E34">A8</font></span></a>, <a class="txt" href="#E10:50"><span class="lab"><font color="Green" title="E36">A10</font></span></a>, <a class="txt" href="#E4:50"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="mesfun7c.html#T31" target="_self" title="MESFUN7C:th.31">Th31</a></span>;<br/>
<a NAME="E16:50"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:50"><span class="lab"><font color="Green" title="E39">A13</font></span></a>, <a class="ref" href="mesfunc6.html#T26" title="MESFUNC6:th.26">MESFUNC6:26</a></span>;<br/>
<a NAME="E17:50"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A15</font></span>: 
 <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun7c.html#T32" target="_self" title="MESFUN7C:th.32">Th32</a></span>;<br/>
<a NAME="E18:50"/>
<span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p1">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="txt" href="#E14:50"><span class="lab"><font color="Green" title="E40">A14</font></span></a>, <a class="txt" href="#E12:50"><span class="lab"><font color="Green" title="E38">A12</font></span></a>, <a class="txt" href="#E10:50"><span class="lab"><font color="Green" title="E36">A10</font></span></a>, <a class="txt" href="#E11:50"><span class="lab"><font color="Green" title="E37">A11</font></span></a>, <a class="ref" href="mesfun7c.html#T31" target="_self" title="MESFUN7C:th.31">Th31</a></span>;<br/>
<a NAME="E19:50"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <span class="p2">(<span class="default"><a href="mesfun6c.html#K2" title="MESFUN6C:func.2">Im</a> <font color="Maroon" title="c4">g</font></span>)</span></span>)</span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:50"><span class="lab"><font color="Green" title="E35">A9</font></span></a>, <a class="txt" href="#E7:50"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="ref" href="mesfunc6.html#T29" title="MESFUNC6:th.29">MESFUNC6:29</a></span>;<br/>
<a NAME="E20:50"/><span class="kw">then </span>
 <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Re</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c4">g</font></span>)</span> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun7c.html#T32" target="_self" title="MESFUN7C:th.32">Th32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:50"/>
<font color="Maroon" title="c3">f</font> <a href="valued_1.html#K19" title="VALUED_1:func.19">(#)</a> <font color="Maroon" title="c4">g</font> <a href="mesfun6c.html#R1" title="MESFUN6C:pred.1">is_measurable_on</a> <font color="Maroon" title="c5">E</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:50"><span class="lab"><font color="Green" title="E41">A15</font></span></a>, <a class="ref" href="mesfun6c.html#D3" title="MESFUN6C:def.3">MESFUN6C:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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