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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Si</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">S</font> be    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">Si</font>;<br/>





<b>assume </b><a NAME="E1:100"/>
<font color="Maroon">S</font> is <a href="prob_1.html#V3">non-decreasing</a>
 ;<br/>

<a NAME="E2:100"/><b>then </b><i><font color="Green">E28</font></i>: 
(  <a href="setlim_1.html#K7" target="_self">lim_sup</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="kurato_2.html#K1">Union</a> <font color="Maroon">S</font> &amp;  <a href="setlim_1.html#K6" target="_self">lim_inf</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="kurato_2.html#K1">Union</a> <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="setlim_1.html#T18" target="_self">Th18</a>, <a class="ref" href="setlim_1.html#T19" target="_self">Th19</a></i>;<br/>
<b>hence </b><a NAME="E3:100"/>
<font color="Maroon">S</font> is <a href="setlim_1.html#V3" target="_self">convergent</a>
 <b>by </b><i><a class="ref" href="setlim_1.html#T12" target="_self">Th12</a></i>;<br/>

<b>hence </b><a NAME="E4:100"/>
 <a href="setlim_1.html#K8" target="_self">lim</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="kurato_2.html#K1">Union</a> <font color="Maroon">S</font>
 <b>by </b><i>, <a class="ref" href="setlim_1.html#T13" target="_self">Th13</a></i>;<br/>


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