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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E57">Th43</font></span>: <a NAME="T43"><span class="comment"><font color="firebrick">:: INTEGR25:43</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><br/>  for <font color="Olive" title="b2">b</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st  <a href="limfunc1.html#K1" title="LIMFUNC1:func.1">left_closed_halfline</a> <font color="Olive" title="b2">b</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="b1">f</font> &amp; <font color="Olive" title="b1">f</font> <a href="integr25.html#R1" title="INTEGR25:pred.1">is_-infty_improper_integrable_on</a> <font color="Olive" title="b2">b</font> holds <br/>(  <a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Olive" title="b1">f</font> <a href="integr25.html#R1" title="INTEGR25:pred.1">is_-infty_improper_integrable_on</a> <font color="Olive" title="b2">b</font> &amp;  <a href="integr25.html#K1" title="INTEGR25:func.1">improper_integral_-infty</a> (<span class="p1">(<span class="default"><a href="valued_1.html#K32" title="VALUED_1:func.32">-</a> <font color="Olive" title="b1">f</font></span>)</span>,<font color="Olive" title="b2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> <span class="p1">(<span class="default"><a href="integr25.html#K1" title="INTEGR25:func.1">improper_integral_-infty</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">b</font>)</span>)</span> )</div></div>
