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<div>:: <span class="kw">deftheorem </span>   defines <a href="cousin2.html#V1" title="COUSIN2:attr.1">HK-integrable</a> <a onclick="hs(this)" href="javascript:()">COUSIN2:def 10 : <br/></a><span> for <font color="Olive" title="b1">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="measure5.html#V2" title="MEASURE5:attr.2">closed_interval</a>  <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><br/>  for <font color="Olive" title="b2">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">I</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> holds <br/> ( <font color="Olive" title="b2">f</font> is  <a href="cousin2.html#V1" title="COUSIN2:attr.1">HK-integrable</a>  iff  ex <font color="Olive" title="b3">J</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> st <br/> for <font color="Olive" title="b4">epsilon</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b4">epsilon</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/> ex <font color="Olive" title="b5">jauge</font> being   <a href="partfun3.html#V1" title="PARTFUN3:attr.1">positive-yielding</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">I</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> st <br/> for <font color="Olive" title="b6">TD</font> being    <a href="cousin.html#M1" title="COUSIN:mode.1">tagged_division</a> of <font color="Olive" title="b1">I</font>  st <font color="Olive" title="b6">TD</font> is <font color="Olive" title="b5">jauge</font> <a href="cousin.html#V1" title="COUSIN:attr.1">-fine</a>  holds <br/><span class="p1"><a href="complex1.html#K9" title="COMPLEX1:func.9">|.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cousin2.html#K8" title="COUSIN2:func.8">tagged_sum</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b6">TD</font>)</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b3">J</font></span>)</span></span><a href="complex1.html#K9" title="COMPLEX1:func.9">.|</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b4">epsilon</font> );<br/></span></div>
