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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: MESFUN11:10</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">f</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#K6" title="NUMBERS:func.6">ExtREAL</a><br/>  for <font color="Olive" title="b4">A</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b2">S</font>  st <font color="Olive" title="b4">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">f</font> holds <br/>( <font color="Olive" title="b3">f</font> is <font color="Olive" title="b4">A</font> <a href="mesfunc1.html#V1" title="MESFUNC1:attr.1">-measurable</a>  iff (  <a href="mesfunc2.html#K1" title="MESFUNC2:func.1">max+</a> <font color="Olive" title="b3">f</font> is <font color="Olive" title="b4">A</font> <a href="mesfunc1.html#V1" title="MESFUNC1:attr.1">-measurable</a>  &amp;  <a href="mesfunc2.html#K2" title="MESFUNC2:func.2">max-</a> <font color="Olive" title="b3">f</font> is <font color="Olive" title="b4">A</font> <a href="mesfunc1.html#V1" title="MESFUNC1:attr.1">-measurable</a>  ) )</div></div>
