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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/>





<a NAME="E1:98"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">A1</font> being  <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>  st <font color="Olive">A1</font> is <a href="prob_1.html#V3">non-decreasing</a> holds <br/> <a href="prob_1.html#K4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Olive">A1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="kurato_2.html#K1">Union</a> <font color="Olive">A1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="98_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">A1</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<br/>

<a NAME="E1:98_1"/>
 <a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a>  <a href="prob_1.html#K4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E2:98_1"/>
( <font color="Maroon">A1</font> is <a href="prob_1.html#V3">non-decreasing</a> implies  <a href="prob_1.html#K4">Intersection</a> <span class="p1">(<span class="default"><a href="setlim_1.html#K2" target="_self">superior_setsequence</a> <font color="Maroon">A1</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="kurato_2.html#K1">Union</a> <font color="Maroon">A1</font> )
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>thus </b><a NAME="E2:98"/>
( <font color="Maroon">S</font> is <a href="prob_1.html#V3">non-decreasing</a> implies  <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> )
 <b>by </b><i><a class="ref" href="setlim_1.html#T19" target="_self">Th19</a></i>;<br/>


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