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<span class="kw">let </span><font color="Maroon" title="c1">X</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">S</font> being  <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">M</font> being  <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <br/> for <font color="Olive" title="b5">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><br/> for <font color="Olive" title="b6">k</font> being  <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Olive" title="b2">M</font>,<font color="Olive" title="b6">k</font> &amp; <font color="Olive" title="b4">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Olive" title="b2">M</font>,<font color="Olive" title="b6">k</font> &amp;  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b2">M</font>,<font color="Olive" title="b6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Olive" title="b4">g</font>,<font color="Olive" title="b2">M</font>,<font color="Olive" title="b6">k</font> holds <br/> <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b3">f</font></span>)</span>,<font color="Olive" title="b2">M</font>,<font color="Olive" title="b6">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b4">g</font></span>)</span>,<font color="Olive" title="b2">M</font>,<font color="Olive" title="b6">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">S</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">X</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">M</font> being  <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c2">S</font><br/> for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <br/> for <font color="Olive" title="b4">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><br/> for <font color="Olive" title="b5">k</font> being  <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b2">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Olive" title="b1">M</font>,<font color="Olive" title="b5">k</font> &amp; <font color="Olive" title="b3">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Olive" title="b1">M</font>,<font color="Olive" title="b5">k</font> &amp;  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">M</font>,<font color="Olive" title="b5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Olive" title="b3">g</font>,<font color="Olive" title="b1">M</font>,<font color="Olive" title="b5">k</font> holds <br/> <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b2">f</font></span>)</span>,<font color="Olive" title="b1">M</font>,<font color="Olive" title="b5">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b3">g</font></span>)</span>,<font color="Olive" title="b1">M</font>,<font color="Olive" title="b5">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">M</font> be   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Maroon" title="c2">S</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">f</font>, <font color="Olive" title="b2">g</font> being  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <br/> for <font color="Olive" title="b3">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><br/> for <font color="Olive" title="b4">k</font> being  <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b4">k</font> &amp; <font color="Olive" title="b2">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b4">k</font> &amp;  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Olive" title="b2">g</font>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b4">k</font> holds <br/> <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b1">f</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b4">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Olive" title="b2">g</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b4">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</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">a</font> being  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a><br/> for <font color="Olive" title="b2">k</font> being  <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b2">k</font> &amp; <font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b2">k</font> &amp;  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b2">k</font> holds <br/> <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b2">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</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">k</font> being  <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>  st <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">k</font> &amp; <font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">k</font> &amp;  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">k</font> holds <br/> <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Olive" title="b1">k</font></span><br/><span class="kw">let </span><font color="Maroon" title="c7">k</font> be   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>; <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="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> &amp; <font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> &amp;  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> implies  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> )</span><br/>













<span class="kw">assume </span><a NAME="E1:62"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
( <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> &amp; <font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> &amp;  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font></span><br/>

<a NAME="E2:62"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A2</font></span>: 
(  ex <font color="Olive" title="b1">E</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">E</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Maroon" title="c4">f</font> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Olive" title="b1">E</font> ) &amp;  ex <font color="Olive" title="b1">E</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">S</font> st <br/>( <font color="Maroon" title="c3">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">E</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E</font> &amp; <font color="Maroon" title="c5">g</font> <a href="mesfunc6.html#R1" title="MESFUNC6:pred.1">is_measurable_on</a> <font color="Olive" title="b1">E</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspace2.html#T35" target="_self" title="LPSPACE2:th.35">EQC00a</a></span>;<br/>
<a NAME="E3:62"/>
<font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="lpspace2.html#T38" target="_self" title="LPSPACE2:th.38">EQC01</a></span>;<br/>
<a NAME="E4:62"/><span class="kw">then </span>
( <font color="Maroon" title="c4">f</font> <a href="lpspace1.html#R1" title="LPSPACE1:pred.1">a.e.=</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c3">M</font> &amp; <font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c4">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> &amp; <font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="lpspace2.html#K1" title="LPSPACE2:func.1">Lp_Functions</a> <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="ref" href="lpspace2.html#T37" target="_self" title="LPSPACE2:th.37">EQC00c</a>, <a class="ref" href="lpspace2.html#T26" target="_self" title="LPSPACE2:th.26">Th01bLp</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:62"/>
 <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K5" title="LPSPACE2:func.5">a.e-eq-class_Lp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>,<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c7">k</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lpspace2.html#T42" target="_self" title="LPSPACE2:th.42">EQC02bx</a>, <a class="ref" href="lpspace1.html#T32" title="LPSPACE1:th.32">LPSPACE1:32</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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