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<b>let </b><font color="Maroon">Omega</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Sigma</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">Omega</font>;<br/><b>let </b><font color="Maroon">ASeq</font> be    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">Sigma</font>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="prob_1.html#M3">Probability</a> of <font color="Maroon">Sigma</font>;<br/>







<b>assume </b><a NAME="E1:41"/>
<font color="Maroon">ASeq</font> is <a href="prob_2.html#V1">disjoint_valued</a>
 ;<br/>

<a NAME="E2:41"/><b>then </b>
<font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">ASeq</font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="series_1.html#K1">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <font color="Maroon">ASeq</font></span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:41"/>
(  <a href="series_1.html#K1">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <font color="Maroon">ASeq</font></span>)</span> is <a href="seq_2.html#V4">convergent</a> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <font color="Maroon">ASeq</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rinfsup1.html#K1">sup</a> <span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <font color="Maroon">ASeq</font></span>)</span></span>)</span> &amp;  <a href="seq_2.html#K2">lim</a> <span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K9">*</a> <font color="Maroon">ASeq</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K1">Union</a> <font color="Maroon">ASeq</font></span>)</span> )
 <b>by </b><i/>;<br/>


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