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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="measure5.html#NM1">Interval</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/>



<b>assume </b><a NAME="E1:62"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K2">-infty</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K1">+infty</a>  &amp; ( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K2" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="measure5.html#K2" target="_self">.[</a></span> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="measure5.html#K1" target="_self">.]</a></span> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K4" target="_self">[.</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="measure5.html#K4" target="_self">.[</a></span> or <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="measure5.html#K3" target="_self">].</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="measure5.html#K3" target="_self">.]</a></span> ) )
 ;<br/>

<a NAME="E2:62"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="supinf_1.html#T29">SUPINF_1:29</a>, <a class="ref" href="supinf_2.html#T19">SUPINF_2:19</a></i>;<br/>
<b>then </b> <a href="measure5.html#K5" target="_self">vol</a> <font color="Maroon">c<sub>1</sub></font> = 
<font color="Maroon">c<sub>3</sub></font> <a href="supinf_2.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="measure5.html#E1:62"><i><font color="Green">E54</font></i></a>, <a class="ref" href="measure5.html#D10" target="_self">Def10</a></i>
<br/>.= 
 <a href="supinf_1.html#K1">+infty</a> 
<b>by </b><i><a class="txt" href="measure5.html#E1:62"><i><font color="Green">E54</font></i></a>, <a class="ref" href="supinf_2.html#T6">SUPINF_2:6</a></i>
;<br/>
<b>hence </b><a NAME="E4:62"/>
 <a href="measure5.html#K5" target="_self">vol</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="supinf_1.html#K1">+infty</a> 
 ;<br/>


</div>
