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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">f</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>, <a href="supinf_1.html#K3" title="SUPINF_1:func.3">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c4">A</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="E1:54"/><i><font color="Green" title="E18">A1</font></i>: 
( <font color="Maroon" title="c3">f</font> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c4">A</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="c3">f</font> )
 ;<br/>

<a NAME="E2:54"/><b>then </b>
 <a href="mesfunc5.html#K1" title="MESFUNC5:func.1">R_EAL</a> <font color="Maroon" title="c3">f</font> <a href="mesfunc1.html#R2" title="MESFUNC1:pred.2">is_measurable_on</a> <font color="Maroon" title="c4">A</font>
 
<b>by </b><i><a class="ref" href="mesfunc6.html#D6" target="_self" title="MESFUNC6:def.6">Def6</a></i>;<br/>
<a NAME="E3:54"/><b>then </b>
<span class="p1"><a href="mesfunc1.html#K12" title="MESFUNC1:func.12">|.</a><span class="default"><span class="p2">(<span class="default"><a href="mesfunc5.html#K1" title="MESFUNC5:func.1">R_EAL</a> <font color="Maroon" title="c3">f</font></span>)</span></span><a href="mesfunc1.html#K12" title="MESFUNC1:func.12">.|</a></span> <a href="mesfunc1.html#R2" title="MESFUNC1:pred.2">is_measurable_on</a> <font color="Maroon" title="c4">A</font>
 
<b>by </b><i><a class="txt" href="mesfunc6.html#E1:54"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="mesfunc2.html#T29" title="MESFUNC2:th.29">MESFUNC2:29</a></i>;<br/>
<a NAME="E4:54"/><b>then </b>
 <a href="mesfunc5.html#K1" title="MESFUNC5:func.1">R_EAL</a> <span class="p1">(<span class="default"><a href="seq_1.html#K21" title="SEQ_1:func.21">abs</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="mesfunc1.html#R2" title="MESFUNC1:pred.2">is_measurable_on</a> <font color="Maroon" title="c4">A</font>
 
<b>by </b><i><a class="ref" href="mesfunc6.html#T44" target="_self" title="MESFUNC6:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E5:54"/>
 <a href="seq_1.html#K21" title="SEQ_1:func.21">abs</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="c4">A</font>
 <b>by </b><i><a class="ref" href="mesfunc6.html#D6" target="_self" title="MESFUNC6:def.6">Def6</a></i>;<br/>


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