<?xml version="1.0"?>
<div class="add">

<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> holds   <a href="lpspace1.html#K20" title="LPSPACE1:func.20">L-1-Space</a> <font color="Olive" title="b2">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K12" title="LPSPACE2:func.12">Lp-Space</a> <font color="Olive" title="b2">M</font>,1</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> holds   <a href="lpspace1.html#K20" title="LPSPACE1:func.20">L-1-Space</a> <font color="Olive" title="b1">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K12" title="LPSPACE2:func.12">Lp-Space</a> <font color="Olive" title="b1">M</font>,1</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">  <a href="lpspace1.html#K20" title="LPSPACE1:func.20">L-1-Space</a> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K12" title="LPSPACE2:func.12">Lp-Space</a> <font color="Maroon" title="c3">M</font>,1</span><br/>





<a NAME="E1:112"/>
 <a href="lpspace1.html#K18" title="LPSPACE1:func.18">Pre-L-Space</a> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K10" title="LPSPACE2:func.10">Pre-Lp-Space</a> <font color="Maroon" title="c3">M</font>,1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspace2.html#T76" target="_self" title="LPSPACE2:th.76">Th009</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:112"/>
 <a href="lpspace1.html#K20" title="LPSPACE1:func.20">L-1-Space</a> <font color="Maroon" title="c3">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lpspace2.html#K12" title="LPSPACE2:func.12">Lp-Space</a> <font color="Maroon" title="c3">M</font>,1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lpspace2.html#T77" target="_self" title="LPSPACE2:th.77">Th10a</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/>


</div>
