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<div>:: <span class="kw">deftheorem </span>   defines <a href="measur13.html#V1" title="MEASUR13:attr.1">sigma_finite</a> <a onclick="hs(this)" href="javascript:()">MEASUR13:def 15 : <br/></a><span> for <font color="Olive" title="b1">m</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">X</font> being   <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  <font color="Olive">b<sub>1</sub></font> <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b3">S</font> being    <a href="measur13.html#M2" title="MEASUR13:mode.2">sigmaFieldFamily</a> of <font color="Olive" title="b2">X</font><br/>  for <font color="Olive" title="b4">M</font> being    <a href="measur13.html#M3" title="MEASUR13:mode.3">sigmaMeasureFamily</a> of <font color="Olive" title="b3">S</font> holds <br/> ( <font color="Olive" title="b4">M</font> is  <a href="measur13.html#V1" title="MEASUR13:attr.1">sigma_finite</a>  iff  for <font color="Olive" title="b5">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b5">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b1">m</font> holds <br/> ex <font color="Olive" title="b6">Xi</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>  ex <font color="Olive" title="b7">Si</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b6">Xi</font> ex <font color="Olive" title="b8">Mi</font> being   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of <font color="Olive" title="b7">Si</font> st <br/>( <font color="Olive" title="b6">Xi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">X</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> &amp; <font color="Olive" title="b7">Si</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">S</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> &amp; <font color="Olive" title="b8">Mi</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">M</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">i</font> &amp; <font color="Olive" title="b8">Mi</font> is  <a href="measur11.html#V4" title="MEASUR11:attr.4">sigma_finite</a>  ) );<br/></span></div>
