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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">M</font> be    <a href="measure1.html#M3" title="MEASURE1:mode.3">sigma_Measure</a> of <font color="Maroon" title="c2">S</font>;<br/><b>let </b><font color="Maroon" title="c4">F</font> be    <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Maroon" title="c2">S</font>;<br/>







<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c4">F</font> is <a href="setlim_1.html#V3" title="SETLIM_1:attr.3">convergent</a> &amp; <font color="Maroon" title="c3">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="Maroon" title="c4">F</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="supinf_1.html#K1" title="SUPINF_1:func.1">+infty</a>  )
 ;<br/>

<a NAME="E2:6"/><b>then </b>
 <a href="setlim_1.html#K7" title="SETLIM_1:func.7">lim_sup</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setlim_1.html#K8" title="SETLIM_1:func.8">lim</a> <font color="Maroon" title="c4">F</font>
 
<b>by </b><i><a class="ref" href="setlim_1.html#D13" title="SETLIM_1:def.13">SETLIM_1:def 13</a></i>;<br/>
<b>hence </b><a NAME="E3:6"/>
 ex <font color="Olive" title="b1">G</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c2">S</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="setlim_1.html#K5" title="SETLIM_1:func.5">@superior_setsequence</a> <font color="Maroon" title="c4">F</font> &amp; <font color="Maroon" title="c3">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#K8" title="SETLIM_1:func.8">lim</a> <font color="Maroon" title="c4">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#K18" title="SUPINF_2:func.18">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">M</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b1">G</font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="mesfunc8.html#E1:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="mesfunc8.html#T4" target="_self" title="MESFUNC8:th.4">Th4</a></i>;<br/>


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