<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E11">Th10</font></span>: <a NAME="T10"><span class="comment"><font color="firebrick">:: MEASURE7:10</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a>  st <font color="Olive" title="b1">G</font> is <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">V99</a>() holds <br/> for <font color="Olive" title="b2">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a><br/>  for <font color="Olive" title="b3">H</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b2">S</font>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <font color="Olive" title="b3">H</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  holds <br/> <a href="supinf_2.html#K17" title="SUPINF_2:func.17">SUM</a> <span class="p1">(<span class="default"><a href="measure7.html#K1" title="MEASURE7:func.1">On</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">G</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">H</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="supinf_2.html#K17" title="SUPINF_2:func.17">SUM</a> <font color="Olive" title="b1">G</font></div></div>
