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<span class="kw">reconsider </span><font color="Maroon" title="c3">X</font> = <font color="Maroon" title="c1">Omega</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">Sigma</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="measure1.html#T7" title="MEASURE1:th.7">MEASURE1:7</a></span>;<br/>
<a NAME="E2:31_1_1"/>
 <a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> (<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">Omega</font>) is <a href="valued_0.html#V3" title="VALUED_0:attr.3">V56</a>()
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc2.html#T28" title="MESFUNC2:th.28">MESFUNC2:28</a></span>;<br/>
<a NAME="E3:31_1_1"/><span class="kw">then </span>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> (<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">Omega</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">Omega</font> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> (<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">Omega</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#D3" title="FUNCT_3:def.3">FUNCT_3:def 3</a>, <a class="ref" href="valued_0.html#D3" title="VALUED_0:def.3">VALUED_0:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">f</font> =  <a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> (<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">Omega</font>) as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Omega</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T2" title="FUNCT_2:th.2">FUNCT_2:2</a></span>;<br/>
<a NAME="E5:31_1_1"/>
(  <a href="mesfunc5.html#K1" title="MESFUNC5:func.1">R_EAL</a> <font color="Maroon" title="c4">f</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> (<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">Omega</font>) &amp;  <a href="mesfunc2.html#K3" title="MESFUNC2:func.3">chi</a> (<font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">Omega</font>) <a href="mesfunc1.html#R1" title="MESFUNC1:pred.1">is_measurable_on</a> <font color="Maroon" title="c3">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc2.html#T29" title="MESFUNC2:th.29">MESFUNC2:29</a></span>;<br/>
<a NAME="E6:31_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">f</font> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c3">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc6.html#D1" title="MESFUNC6:def.1">MESFUNC6:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:31_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">Omega</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ex <font color="Olive" title="b2">X</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">Sigma</font> st <br/>( <font color="Olive" title="b2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">Omega</font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Olive" title="b2">X</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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