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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E53">Th79</font></span>: <a NAME="T79"><span class="comment"><font color="firebrick">:: DBLSEQ_3:79</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font> being  <a href="mesfunc5.html#V3" title="MESFUNC5:attr.3">V183</a>() <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> holds <br/> (  <a href="dblseq_3.html#K11" title="DBLSEQ_3:func.11">Partial_Sums</a> <font color="Olive" title="b1">f</font> is  <a href="dblseq_3.html#V6" title="DBLSEQ_3:attr.6">convergent_in_cod1_to_finite</a>  iff  <a href="dblseq_3.html#K10" title="DBLSEQ_3:func.10">Partial_Sums_in_cod1</a> <font color="Olive" title="b1">f</font> is  <a href="dblseq_3.html#V6" title="DBLSEQ_3:attr.6">convergent_in_cod1_to_finite</a>  )</div></div>
