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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E34">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: INTEGR25:27</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>  holds <br/>(  not <font color="Olive" title="b1">f</font> <a href="integr25.html#R2" title="INTEGR25:pred.2">is_+infty_improper_integrable_on</a> <font color="Olive" title="b2">b</font> or ( <font color="Olive" title="b1">f</font> <a href="integr10.html#R3" title="INTEGR10:pred.3">is_+infty_ext_Riemann_integrable_on</a> <font color="Olive" title="b2">b</font> &amp;  <a href="integr25.html#K2" title="INTEGR25:func.2">improper_integral_+infty</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="integr10.html#K3" title="INTEGR10:func.3">infty_ext_right_integral</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">b</font>) ) or (  not <font color="Olive" title="b1">f</font> <a href="integr10.html#R3" title="INTEGR10:pred.3">is_+infty_ext_Riemann_integrable_on</a> <font color="Olive" title="b2">b</font> &amp;  <a href="integr25.html#K2" title="INTEGR25:func.2">improper_integral_+infty</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  ) or (  not <font color="Olive" title="b1">f</font> <a href="integr10.html#R3" title="INTEGR10:pred.3">is_+infty_ext_Riemann_integrable_on</a> <font color="Olive" title="b2">b</font> &amp;  <a href="integr25.html#K2" title="INTEGR25:func.2">improper_integral_+infty</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">b</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K2" title="XXREAL_0:func.2">-infty</a>  ) )</div></div>
