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<b>let </b><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> ;<br/><b>let </b><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>;<br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="measure1.html#M3" title="MEASURE1:mode.3">sigma_Measure</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">f</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#K6" title="NUMBERS:func.6">ExtREAL</a> ;<br/>







<b>assume </b><a NAME="E1:69"/><i><font color="Green" title="E66">A1</font></i>: 
 ex <font color="Olive" title="b1">A</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c5">c</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>;<br/><b>let </b><font color="Maroon" title="c6">B</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font>;<br/>



<b>assume </b><a NAME="E2:69"/><i><font color="Green" title="E67">A2</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="mesfunc1.html#R2" title="MESFUNC1:pred.2">is_measurable_on</a> <font color="Maroon" title="c6">B</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c7">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font><b> such that </b><br/><a NAME="E4:69"/><i><font color="Green" title="E68">A3</font></i>: 
<font color="Maroon" title="c7">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E1:69"><i><font color="Green" title="E66">A1</font></i></a></i>;<br/>
<a NAME="E5:69"/><i><font color="Green" title="E69">A4</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="mesfunc1.html#R2" title="MESFUNC1:pred.2">is_measurable_on</a> <font color="Maroon" title="c7">A</font> <a href="measure1.html#K3" title="MEASURE1:func.3">/\</a> <font color="Maroon" title="c6">B</font>
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E4:69"><i><font color="Green" title="E68">A3</font></i></a>, <a class="txt" href="mesfunc5.html#E2:69"><i><font color="Green" title="E67">A2</font></i></a>, <a class="ref" href="mesfunc5.html#T54" target="_self" title="MESFUNC5:th.54">Th54</a></i>;<br/>
<a NAME="E6:69"/>
<font color="Maroon" title="c7">A</font> <a href="measure1.html#K3" title="MEASURE1:func.3">/\</a> <font color="Maroon" title="c6">B</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">f</font>
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E4:69"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E7:69"/><b>then </b><i><font color="Green" title="E70">A5</font></i>: 
<font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K8" title="MESFUNC1:func.8">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc1.html#R2" title="MESFUNC1:pred.2">is_measurable_on</a> <font color="Maroon" title="c7">A</font> <a href="measure1.html#K3" title="MEASURE1:func.3">/\</a> <font color="Maroon" title="c6">B</font>
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E5:69"><i><font color="Green" title="E69">A4</font></i></a>, <a class="ref" href="mesfunc1.html#T41" title="MESFUNC1:th.41">MESFUNC1:41</a></i>;<br/>
<a NAME="E8:69"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K8" title="MESFUNC1:func.8">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">A</font>
 
<b>by </b><i><a class="txt" href="mesfunc5.html#E4:69"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="mesfunc1.html#D6" title="MESFUNC1:def.6">MESFUNC1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E9:69"/>
<font color="Maroon" title="c5">c</font> <a href="mesfunc1.html#K8" title="MESFUNC1:func.8">(#)</a> <font color="Maroon" title="c4">f</font> <a href="mesfunc1.html#R2" title="MESFUNC1:pred.2">is_measurable_on</a> <font color="Maroon" title="c6">B</font>
 <b>by </b><i><a class="txt" href="mesfunc5.html#E7:69"><i><font color="Green" title="E70">A5</font></i></a>, <a class="ref" href="mesfunc5.html#T54" target="_self" title="MESFUNC5:th.54">Th54</a></i>;<br/>


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