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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E17">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: FINANCE1:12</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">F</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="b3">d</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">d</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> for <font color="Olive" title="b4">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b5">phi</font> being   <a href="seq_1.html#NM1" title="SEQ_1:NM.1">Real_Sequence</a><br/>  for <font color="Olive" title="b6">G</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">sequence</a> of <span class="p1">(<span class="default"><a href="finance1.html#K6" title="FINANCE1:func.6">set_of_random_variables_on</a> (<font color="Olive" title="b2">F</font>,<a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a>)</span>)</span>  st  <a href="finance1.html#K9" title="FINANCE1:func.9">Element_Of</a> (<font color="Olive" title="b2">F</font>,<a href="prob_1.html#K12" title="PROB_1:func.12">Borel_Sets</a>,<font color="Olive" title="b6">G</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>) <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">Omega</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b4">r</font></span>)</span> holds <br/> for <font color="Olive" title="b7">w</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">Omega</font> holds   <a href="finance1.html#K11" title="FINANCE1:func.11">PortfolioValueFutExt</a> (<font color="Olive" title="b3">d</font>,<font color="Olive" title="b5">phi</font>,<font color="Olive" title="b2">F</font>,<font color="Olive" title="b6">G</font>,<font color="Olive" title="b7">w</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b4">r</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b5">phi</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="finance1.html#K12" title="FINANCE1:func.12">PortfolioValueFut</a> (<font color="Olive" title="b3">d</font>,<font color="Olive" title="b5">phi</font>,<font color="Olive" title="b2">F</font>,<font color="Olive" title="b6">G</font>,<font color="Olive" title="b7">w</font>)</span>)</span></div></div>
