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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">LM1</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: LOPBAN13:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="lopban_2.html#NM3" title="LOPBAN_2:NM.3">Banach_Algebra</a><br/>  for <font color="Olive" title="b2">z</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">X</font>  st <span class="p1"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b2">z</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 holds <br/>( <font color="Olive" title="b2">z</font> <a href="lopban_3.html#K5" title="LOPBAN_3:func.5">GeoSeq</a>  is  <a href="lopban_3.html#V2" title="LOPBAN_3:attr.2">norm_summable</a>  &amp; <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> <span class="p3">(<span class="default"><font color="Olive" title="b2">z</font> <a href="lopban_3.html#K5" title="LOPBAN_3:func.5">GeoSeq</a></span>)</span></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> 1 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2"><a href="normsp_0.html#K2" title="NORMSP_0:func.2">||.</a><span class="default"><font color="Olive" title="b2">z</font></span><a href="normsp_0.html#K2" title="NORMSP_0:func.2">.||</a></span></span>)</span> )</div></div>
