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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="numbers.html#K6">ExtREAL</a> ;<br/><b>let </b><font color="Maroon">g</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">X</font>, <a href="numbers.html#K6">ExtREAL</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">S</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:12"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">f</font> <a href="mesfunc2.html#R1" target="_self">is_finite</a> 
 <b>and </b><br/><a NAME="E2:12"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">g</font> <a href="mesfunc2.html#R1" target="_self">is_finite</a> 
 <b>and </b><br/><a NAME="E3:12"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">f</font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E4:12"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">g</font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 <b>and </b><br/><a NAME="E5:12"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">g</font>
 ;<br/>

<a NAME="E6:12"/>
( <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="mesfunc1.html#K8">(#)</a> <font color="Maroon">g</font> <a href="mesfunc2.html#R1" target="_self">is_finite</a>  &amp; <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="mesfunc1.html#K8">(#)</a> <font color="Maroon">g</font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font> )
 
<b>by </b><i>, , , , <a class="ref" href="mesfunc1.html#T41">MESFUNC1:41</a></i>;<br/>
<a NAME="E7:12"/><b>then </b>
(  <a href="mesfunc1.html#K9">-</a> <font color="Maroon">g</font> <a href="mesfunc2.html#R1" target="_self">is_finite</a>  &amp;  <a href="mesfunc1.html#K9">-</a> <font color="Maroon">g</font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E8:12"/><b>then </b>
<font color="Maroon">f</font> <a href="mesfunc1.html#K13">+</a> <span class="p1">(<span class="default"><a href="mesfunc1.html#K9">-</a> <font color="Maroon">g</font></span>)</span> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E9:12"/>
<font color="Maroon">f</font> <a href="mesfunc1.html#K6">-</a> <font color="Maroon">g</font> <a href="mesfunc1.html#R2">is_measurable_on</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>


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