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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">Th50</font></span>: <a NAME="T50"><span class="comment"><font color="firebrick">:: MESFUN16:50</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">J</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="struct_0.html#NM12" title="STRUCT_0:NM.12">PartFunc</a> of <span class="p1"><a href="prvect_3.html#K9" title="PRVECT_3:func.9">[:</a><span class="default"><a href="dualsp02.html#K3" title="DUALSP02:func.3">RNS_Real</a>,<a href="dualsp02.html#K3" title="DUALSP02:func.3">RNS_Real</a></span><a href="prvect_3.html#K9" title="PRVECT_3:func.9">:]</a></span>,<a href="dualsp02.html#K3" title="DUALSP02:func.3">RNS_Real</a><br/>  for <font color="Olive" title="b4">g</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b5">E</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_1.html#K9" title="PROB_1:func.9">sigma</a> <span class="p1">(<span class="default"><a href="measur10.html#K3" title="MEASUR10:func.3">measurable_rectangles</a> (<a href="measur12.html#K14" title="MEASUR12:func.14">L-Field</a>,<a href="measur12.html#K14" title="MEASUR12:func.14">L-Field</a>)</span>)</span>  st <span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">f</font> &amp; <font color="Olive" title="b3">f</font> <a href="nfcont_1.html#R3" title="NFCONT_1:pred.3">is_continuous_on</a> <span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span> &amp; <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">g</font> &amp; <font color="Olive" title="b5">E</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="mcart_1.html#K8" title="MCART_1:func.8">[:</a><span class="default"><font color="Olive" title="b1">I</font>,<font color="Olive" title="b2">J</font></span><a href="mcart_1.html#K8" title="MCART_1:func.8">:]</a></span> holds <br/><font color="Olive" title="b4">g</font> is <font color="Olive" title="b5">E</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a> </div></div>
