<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th41</font></span>: <a NAME="T41"><span class="comment"><font color="firebrick">:: MEASURE6:41</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> holds <br/> ( <font color="Olive" title="b1">X</font> is  <a href="xxreal_2.html#V4" title="XXREAL_2:attr.4">bounded_above</a>  iff  <a href="measure6.html#K3" title="MEASURE6:func.3">--</a> <font color="Olive" title="b1">X</font> is  <a href="xxreal_2.html#V3" title="XXREAL_2:attr.3">bounded_below</a>  )</div></div>
