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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: INTEGRA4:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</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="b2">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b2">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">A</font> is  <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">bounded</a>  holds <br/>( <font color="Olive" title="b2">f</font> is  <a href="integra1.html#V1" title="INTEGRA1:attr.1">upper_integrable</a>  &amp; <font color="Olive" title="b2">f</font> is  <a href="integra1.html#V2" title="INTEGRA1:attr.2">lower_integrable</a>  )</div></div>
