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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E47">Th42</font></span>: <a NAME="T42"><span class="comment"><font color="firebrick">:: LPSPACC1:42</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">M</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a><br/>  for <font color="Olive" title="b6">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="lpspacc1.html#K22" title="LPSPACC1:func.22">Pre-L-CSpace</a> <font color="Olive" title="b3">M</font></span>)</span>  st <font color="Olive" title="b4">f</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b6">x</font> &amp; <font color="Olive" title="b5">g</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b6">x</font> holds <br/>( <font color="Olive" title="b4">f</font> <a href="lpspacc1.html#R1" title="LPSPACC1:pred.1">a.e.cpfunc=</a> <font color="Olive" title="b5">g</font>,<font color="Olive" title="b3">M</font> &amp;  <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Olive" title="b3">M</font>,<font color="Olive" title="b4">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfun6c.html#K1" title="MESFUN6C:func.1">Integral</a> (<font color="Olive" title="b3">M</font>,<font color="Olive" title="b5">g</font>) &amp;  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Olive" title="b3">M</font>,<span class="p1">(<span class="default"><a href="valued_1.html#K56" title="VALUED_1:func.56">abs</a> <font color="Olive" title="b4">f</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<font color="Olive" title="b3">M</font>,<span class="p1">(<span class="default"><a href="valued_1.html#K56" title="VALUED_1:func.56">abs</a> <font color="Olive" title="b5">g</font></span>)</span>) )</div></div>
