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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>, <a href="supinf_1.html#K3">REAL</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>;<br/>







<b>assume </b><a NAME="E1:54"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">f</font> <a href="mesfunc6.html#R1" target="_self">is_measurable_on</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> )
 ;<br/>

<a NAME="E2:54"/><b>then </b>
 <a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:54"/><b>then </b>
<span class="p1"><a href="mesfunc1.html#K12">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfunc5.html#K1">R_EAL</a> <font color="Maroon">f</font></span>)</span></span><a href="mesfunc1.html#K12">.|</a></span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="mesfunc2.html#T29">MESFUNC2:29</a></i>;<br/>
<a NAME="E4:54"/><b>then </b>
 <a href="mesfunc5.html#K1">R_EAL</a> <span class="p1">(<span class="default"><a href="seq_1.html#K21">abs</a> <font color="Maroon">f</font></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:54"/>
 <a href="seq_1.html#K21">abs</a> <font color="Maroon">f</font> <a href="mesfunc6.html#R1" target="_self">is_measurable_on</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>


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