<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T78"><span class="comment"><font color="firebrick">:: MESFUNC6:78</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</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">S</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b1">X</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="Olive" title="b1">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="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">S</font>  st <font color="Olive" title="b5">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b4">g</font></span>)</span> &amp; <font color="Olive" title="b3">f</font> is <font color="Olive" title="b5">A</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <font color="Olive" title="b4">g</font> is <font color="Olive" title="b5">A</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  holds <br/><span class="p1">(<span class="default"><a href="rfunct_3.html#K19" title="RFUNCT_3:func.19">max-</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Olive" title="b4">g</font></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rfunct_3.html#K18" title="RFUNCT_3:func.18">max+</a> <font color="Olive" title="b3">f</font></span>)</span> is <font color="Olive" title="b5">A</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a> </div></div>
