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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="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Sigma</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font><br/>  for <font color="Olive" title="b2">f</font> being    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of <font color="Olive" title="b1">Sigma</font><br/>  for <font color="Olive" title="b3">r</font> being   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">r</font> holds <br/><span class="p1">(<span class="default"><a href="random_1.html#K7" title="RANDOM_1:func.7">abs</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> <font color="Olive" title="b3">r</font> is    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of <font color="Olive" title="b1">Sigma</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">Sigma</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">f</font> being    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of <font color="Maroon" title="c2">Sigma</font><br/>  for <font color="Olive" title="b2">r</font> being   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">r</font> holds <br/><span class="p1">(<span class="default"><a href="random_1.html#K7" title="RANDOM_1:func.7">abs</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> <font color="Olive" title="b2">r</font> is    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of <font color="Maroon" title="c2">Sigma</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">f</font> be    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of <font color="Maroon" title="c2">Sigma</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">r</font> being   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">r</font> holds <br/><span class="p1">(<span class="default"><a href="random_1.html#K7" title="RANDOM_1:func.7">abs</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> <font color="Olive" title="b1">r</font> is    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of <font color="Maroon" title="c2">Sigma</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">r</font> be   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">r</font> implies <span class="p1">(<span class="default"><a href="random_1.html#K7" title="RANDOM_1:func.7">abs</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> <font color="Maroon" title="c4">r</font> is    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of <font color="Maroon" title="c2">Sigma</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:45"/><span class="lab"><font color="Green" title="E34">A1</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">r</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="random_1.html#K7" title="RANDOM_1:func.7">abs</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> <font color="Maroon" title="c4">r</font> is    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of <font color="Maroon" title="c2">Sigma</font></span><br/>

<a NAME="E2:45"/>
 <a href="random_1.html#K7" title="RANDOM_1:func.7">abs</a> <font color="Maroon" title="c3">f</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="random_1.html#E37"><span class="lab"><font color="Green" title="E32">Lm13</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:45"/>
<span class="p1">(<span class="default"><a href="random_1.html#K7" title="RANDOM_1:func.7">abs</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> <font color="Maroon" title="c4">r</font> is    <a href="random_1.html#M1" title="RANDOM_1:mode.1">Real-Valued-Random-Variable</a> of <font color="Maroon" title="c2">Sigma</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:45"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <a class="ref" href="random_1.html#T23" target="_self" title="RANDOM_1:th.23">Th23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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