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<div><span class="kw">theorem </span><a NAME="T21"><span class="comment"><font color="firebrick">:: INTEGR16:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">c</font> being   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a><br/>  for <font color="Olive" title="b2">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="b3">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  st <font color="Olive" title="b2">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> &amp; <font color="Olive" title="b3">f</font> <a href="integr16.html#R1" title="INTEGR16:pred.1">is_integrable_on</a> <font color="Olive" title="b2">A</font> &amp; <font color="Olive" title="b3">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b2">A</font> is  <a href="comseq_2.html#V1" title="COMSEQ_2:attr.1">bounded</a>  holds <br/>( <font color="Olive" title="b1">c</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Olive" title="b3">f</font> <a href="integr16.html#R1" title="INTEGR16:pred.1">is_integrable_on</a> <font color="Olive" title="b2">A</font> &amp;  <a href="integr16.html#K7" title="INTEGR16:func.7">integral</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">c</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Olive" title="b3">f</font></span>)</span>,<font color="Olive" title="b2">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">c</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="integr16.html#K7" title="INTEGR16:func.7">integral</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b2">A</font>)</span>)</span> )</div></div>
