https://companal.subwiki.org/w/index.php?action=history&feed=atom&title=Morera%27s_theoremMorera's theorem - Revision history2026-05-13T11:38:07ZRevision history for this page on the wikiMediaWiki 1.41.2https://companal.subwiki.org/w/index.php?title=Morera%27s_theorem&diff=330&oldid=prevVipul: 1 revision2008-05-18T19:16:49Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://companal.subwiki.org/w/index.php?title=Morera%27s_theorem&diff=329&oldid=prevVipul: New page: {{basic fact}} ==Statement== Suppose <math>U</math> is a domain (open connected subset) in <math>\mathbb{C}</math> and <math>f:U \to \mathbb{C}</math> is a continuous function with t...2008-04-26T19:02:27Z<p>New page: {{basic fact}} ==Statement== Suppose <math>U</math> is a <a href="/wiki/Domain" title="Domain">domain</a> (open connected subset) in <math>\mathbb{C}</math> and <math>f:U \to \mathbb{C}</math> is a continuous function with t...</p>
<p><b>New page</b></p><div>{{basic fact}}<br />
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==Statement==<br />
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Suppose <math>U</math> is a [[domain]] (open connected subset) in <math>\mathbb{C}</math> and <math>f:U \to \mathbb{C}</math> is a continuous function with the property that for every triangle <math>\triangle \subset U</math>, we have:<br />
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<math>\int_{\partial \triangle} f(z) dz = 0</math><br />
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Then, <math>f</math> is a holomorphic function.<br />
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==Related facts==<br />
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* [[Goursat's integral lemma]] is a converse of sorts</div>Vipul