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<div><span class="kw">theorem </span><a NAME="T25"><span class="comment"><font color="firebrick">:: MESFUN13:25</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">E</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b5">f</font> being  <font color="Olive">b<sub>4</sub></font> <a href="mesfunc1.html#V1" title="MESFUNC1:attr.1">-measurable</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">X</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a>  st  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b5">f</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">E</font> &amp; <font color="Olive" title="b5">f</font> <a href="mesfun13.html#R1" title="MESFUN13:pred.1">is_a.e.integrable_on</a> <font color="Olive" title="b3">M</font> holds <br/><font color="Olive" title="b5">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a> <font color="Olive" title="b3">M</font></div></div>
