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<div><span class="kw">theorem </span><a NAME="T47"><span class="comment"><font color="firebrick">:: MESFUN14:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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#K6" title="NUMBERS:func.6">ExtREAL</a>  st <font color="Olive" title="b1">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a>  <a href="measur12.html#K13" title="MEASUR12:func.13">B-Meas</a>  holds <br/>( <font color="Olive" title="b1">f</font> <a href="mesfunc5.html#R1" title="MESFUNC5:pred.1">is_integrable_on</a>  <a href="measur12.html#K15" title="MEASUR12:func.15">L-Meas</a>  &amp;  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<a href="measur12.html#K13" title="MEASUR12:func.13">B-Meas</a>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc5.html#K7" title="MESFUNC5:func.7">Integral</a> (<a href="measur12.html#K15" title="MEASUR12:func.15">L-Meas</a>,<font color="Olive" title="b1">f</font>) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfun14.html#T38" target="_self" onmouseover="rs('mesfun14/T38')" onmouseout="rh()">Th38</a>, <a class="ref" href="measur12.html#D11" onmouseover="rs('measur12/D11')" onmouseout="rh()">MEASUR12:def 11</a>, <a class="ref" href="measur12.html#D12" onmouseover="rs('measur12/D12')" onmouseout="rh()">MEASUR12:def 12</a></span>;<br/></div></div>
