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<div><span class="kw">theorem </span><a NAME="T83"><span class="comment"><font color="firebrick">:: MESFUN15:83</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#K1" title="NUMBERS:func.1">REAL</a>  st  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  &amp; <font color="Olive" title="b1">f</font> <a href="integr25.html#R3" title="INTEGR25:pred.3">is_improper_integrable_on_REAL</a>  &amp;  <a href="valued_1.html#K56" title="VALUED_1:func.56">abs</a> <font color="Olive" title="b1">f</font> is  <a href="integr10.html#V1" title="INTEGR10:attr.1">infty_ext_Riemann_integrable</a>  holds <br/>( <font color="Olive" title="b1">f</font> <a href="mesfunc6.html#R2" title="MESFUNC6:pred.2">is_integrable_on</a>  <a href="measur12.html#K15" title="MEASUR12:func.15">L-Meas</a>  &amp;  <a href="integr25.html#K3" title="INTEGR25:func.3">improper_integral_on_REAL</a> <font color="Olive" title="b1">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mesfunc6.html#K1" title="MESFUNC6:func.1">Integral</a> (<a href="measur12.html#K15" title="MEASUR12:func.15">L-Meas</a>,<font color="Olive" title="b1">f</font>) )</div></div>
