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<div><span class="kw">theorem </span><a NAME="T21"><span class="comment"><font color="firebrick">:: INTEGR23:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">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="b2">rho</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">A</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b3">u</font> being   <a href="fcont_1.html#V1" title="FCONT_1:attr.1">continuous</a>  <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 <font color="Olive" title="b2">rho</font> is  <a href="integr22.html#V1" title="INTEGR22:attr.1">bounded_variation</a>  &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b3">u</font> <a href="integr22.html#R1" title="INTEGR22:pred.1">is_RiemannStieltjes_integrable_with</a> <font color="Olive" title="b2">rho</font></div></div>
