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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E49">Th46</font></span>: <a NAME="T48"><span class="comment"><font color="firebrick">:: MEASURE9:48</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S</font> being   <a href="simplex0.html#NV1" title="SIMPLEX0:NV.1">with_empty_element</a>   <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">cap-closed</a>   <a href="srings_3.html#V1" title="SRINGS_3:attr.1">semi-diff-closed</a>  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">P</font> being    <a href="measure9.html#M1" title="MEASURE9:mode.1">pre-Measure</a> of <font color="Olive" title="b2">S</font>  ex <font color="Olive" title="b4">M</font> being   <a href="valued_0.html#V10" title="VALUED_0:attr.10">zeroed</a>  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">V224</a>()  <a href="measure1.html#V2" title="MEASURE1:attr.2">additive</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="srings_3.html#K1" title="SRINGS_3:func.1">Ring_generated_by</a> <font color="Olive" title="b2">S</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> st <br/> for <font color="Olive" title="b5">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b5">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="srings_3.html#K1" title="SRINGS_3:func.1">Ring_generated_by</a> <font color="Olive" title="b2">S</font> holds <br/> for <font color="Olive" title="b6">F</font> being   <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Olive" title="b2">S</font>  st <font color="Olive" title="b5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b6">F</font> holds <br/><font color="Olive" title="b4">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Olive" title="b5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extreal1.html#K4" title="EXTREAL1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">P</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">*</a> <font color="Olive" title="b6">F</font></span>)</span></div></div>
