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<div><span class="kw">theorem </span><a NAME="T6"><span class="comment"><font color="firebrick">:: MESFUNC8:6</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">M</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">F</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Olive" title="b2">S</font>  st <font color="Olive" title="b4">F</font> is  <a href="kurato_0.html#V3" title="KURATO_0:attr.3">convergent</a>  &amp; <font color="Olive" title="b3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><a href="card_3.html#K3" title="CARD_3:func.3">Union</a> <font color="Olive" title="b4">F</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  holds <br/> ex <font color="Olive" title="b5">G</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <font color="Olive" title="b2">S</font> st <br/>( <font color="Olive" title="b5">G</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="setlim_1.html#K6" title="SETLIM_1:func.6">superior_setsequence</a> <font color="Olive" title="b4">F</font> &amp; <font color="Olive" title="b3">M</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><a href="setlim_1.html#NK7" title="SETLIM_1:NK.7">lim</a> <font color="Olive" title="b4">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K7" title="SUPINF_2:func.7">inf</a> <span class="p1">(<span class="default"><a href="supinf_2.html#K15" title="SUPINF_2:func.15">rng</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b5">G</font></span>)</span></span>)</span> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc8.html#T4" target="_self" onmouseover="rs('mesfunc8/T4')" onmouseout="rh()">Th4</a></span>;<br/></div></div>
