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<div><span class="kw">theorem </span><a NAME="T36"><span class="comment"><font color="firebrick">:: RANDOM_1:36</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Omega</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">Sigma</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b1">Omega</font><br/>  for <font color="Olive" title="b4">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Olive" title="b3">Sigma</font><br/>  for <font color="Olive" title="b5">X</font> being   <a href="random_1.html#NM1" title="RANDOM_1:NM.1">Real-Valued-Random-Variable</a> of <font color="Olive" title="b3">Sigma</font>  st  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">r</font> &amp; <font color="Olive" title="b5">X</font> is  <a href="supinf_2.html#V6" title="SUPINF_2:attr.6">nonnegative</a>  &amp; <font color="Olive" title="b5">X</font> <a href="random_1.html#R1" title="RANDOM_1:pred.1">is_integrable_on</a> <font color="Olive" title="b4">P</font> holds <br/><font color="Olive" title="b4">P</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b6">t</font> where <font color="Olive" title="b6">t</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">Omega</font> : <font color="Olive" title="b2">r</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b5">X</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">t</font> </span> } </span>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="random_1.html#K8" title="RANDOM_1:func.8">expect</a> (<font color="Olive" title="b5">X</font>,<font color="Olive" title="b4">P</font>)</span>)</span> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <font color="Olive" title="b2">r</font></div></div>
