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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">C</font> be    <a href="measure4.html#M1" target="_self">C_Measure</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="measure3.html#D2">MEASURE3:def 2</a><br/><b>let </b><font color="Maroon">B</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:28"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E2:28"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> &amp; <span class="p1">(<span class="default"><a href="measure4.html#K5" target="_self">sigma_Meas</a> <font color="Maroon">C</font></span>)</span> <a href="supinf_2.html#K13">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a>  )
 ;<br/>

<b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">B</font> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="txt" href="measure4.html#E2:28"><i><font color="Green">E24</font></i></a></i>;<br/>
<a NAME="E4:28"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i><a class="txt" href="measure4.html#E2:28"><i><font color="Green">E24</font></i></a>, <a class="txt" href="measure4.html#E4:28"><i><font color="Green">E25</font></i></a>, </i>;<br/>
<a NAME="E5:28"/>
<font color="Maroon">C</font> is <a href="supinf_2.html#V6">nonnegative</a>
 
<b>by </b><i/>;<br/>
<a NAME="E6:28"/><b>then </b>
(  <a href="supinf_2.html#K1">0.</a>  <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">A</font> &amp; <font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">A</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_2.html#K1">0.</a>  )
 
<b>by </b><i><a class="txt" href="measure4.html#E4:28"><i><font color="Green">E25</font></i></a>, , , <a class="ref" href="measure1.html#D4">MEASURE1:def 4</a></i>;<br/>
<a NAME="E7:28"/><b>then </b>
<font color="Maroon">C</font> <a href="measure1.html#K1">.</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a> 
 
<b>by </b><i><a class="ref" href="supinf_1.html#T22">SUPINF_1:22</a></i>;<br/>
<b>hence </b><a NAME="E8:28"/>
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="measure4.html#K1" target="_self">sigma_Field</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="txt" href="measure4.html#E1:28"><i><font color="Green">E23</font></i></a></i>;<br/>


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