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<span class="kw">let </span><font color="Maroon" title="c1">Omega</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">P</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">Omega</font><br/> for <font color="Olive" title="b2">X</font> being   <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">Omega</font> holds  <font color="Olive" title="b2">X</font> <a href="random_1.html#R1" title="RANDOM_1:pred.1">is_integrable_on</a> <font color="Olive" title="b1">P</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">P</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">Omega</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">X</font> being   <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">Omega</font> holds  <font color="Olive" title="b1">X</font> <a href="random_1.html#R1" title="RANDOM_1:pred.1">is_integrable_on</a> <font color="Maroon" title="c2">P</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">X</font> be    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">Omega</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">X</font> <a href="random_1.html#R1" title="RANDOM_1:pred.1">is_integrable_on</a> <font color="Maroon" title="c2">P</font></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">M</font> =  <a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c2">P</font>;<br/>
<a NAME="E1:53"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">Omega</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E2:53"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c2">P</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#D13" title="PROB_1:def.13">PROB_1:def 13</a></span>;<br/>
<a NAME="E3:53"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c2">P</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">X</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T9" title="XXREAL_0:th.9">XXREAL_0:9</a></span>;<br/>
<a NAME="E4:53"/><span class="kw">then </span>
<font color="Maroon" title="c3">X</font> <a href="mesfunc6.html#R3" title="MESFUNC6:pred.3">is_integrable_on</a>  <a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c2">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="random_1.html#E9"><span class="lab"><font color="Green" title="E8">Lm5</font></span></a>, <a class="ref" href="random_1.html#T6" target="_self" title="RANDOM_1:th.6">Th6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:53"/>
<font color="Maroon" title="c3">X</font> <a href="random_1.html#R1" title="RANDOM_1:pred.1">is_integrable_on</a> <font color="Maroon" title="c2">P</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="random_1.html#D3" target="_self" title="RANDOM_1:def.3">Def3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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