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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">LM0</font></span>: <a NAME="T2"><span class="comment"><font color="firebrick">:: LOPBAN13:2</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="lopban_1.html#NM2" title="LOPBAN_1:NM.2">RealBanachSpace</a><br/>  for <font color="Olive" title="b2">s</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b2">s</font> is  <a href="lopban_3.html#V2" title="LOPBAN_3:attr.2">norm_summable</a>  holds <br/><span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><span class="p2">(<span class="default"><a href="lopban_3.html#K1" title="LOPBAN_3:func.1">Sum</a> <font color="Olive" title="b2">s</font></span>)</span></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1"><a href="normsp_0.html#K5" title="NORMSP_0:func.5">||.</a><span class="default"><font color="Olive" title="b2">s</font></span><a href="normsp_0.html#K5" title="NORMSP_0:func.5">.||</a></span></div></div>
