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<div class="add">

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">M</font> be    <a href="measure1.html#M3" target="_self">sigma_Measure</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">T</font> be   <a href="measure1.html#NM3">N_Sub_set_fam</a> of <font color="Maroon">X</font>;<br/>







<b>assume </b><a NAME="E1:66"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">A</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font> holds <br/><font color="Olive">A</font> <a href="measure1.html#R2" target="_self">is_measurable</a> <font color="Maroon">M</font>
 ;<br/>

<a NAME="E2:66"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">T</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">S</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:66_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 ;<br/>

<a NAME="E2:66_1"/><b>then </b>
<font color="Maroon">x</font> <a href="measure1.html#R2" target="_self">is_measurable</a> <font color="Maroon">M</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:66_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 <b>by </b><i><a class="ref" href="measure1.html#T9" target="_self">Th9</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:66"/><b>then </b><i><font color="Green">E25</font></i>: 
 <a href="setfam_1.html#K5">union</a> <font color="Maroon">T</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:66"/>
 <a href="setfam_1.html#K6">meet</a> <font color="Maroon">T</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 
<b>by </b><i>, <a class="txt" href="measure1.html#E2:66"><i><font color="Green">E24</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:66"/>
(  <a href="setfam_1.html#K5">union</a> <font color="Maroon">T</font> <a href="measure1.html#R2" target="_self">is_measurable</a> <font color="Maroon">M</font> &amp;  <a href="setfam_1.html#K6">meet</a> <font color="Maroon">T</font> <a href="measure1.html#R2" target="_self">is_measurable</a> <font color="Maroon">M</font> )
 <b>by </b><i>, <a class="ref" href="measure1.html#T9" target="_self">Th9</a></i>;<br/>


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