Morera's theorem


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Morera's theorem

[mȯ′rer·əz ‚thir·əm]
(mathematics)
If a function of a complex variable is continuous in a simply connected domain D, and if the integral of the function about every simply connected curve in D vanishes, then the function is analytic in D.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Now, by Morera's theorem with aids of Holder's inequality and the dominated convergence theorem, we have (30) for [lambda] [member of] [C.sub.+].
By Morera's theorem and the dominated convergence theorem we have the theorem.