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单词 Montel's Theorem
释义

Montel's Theorem

Let be an analytic function of , regular in the half-strip defined by and . If isbounded in and tends to a limit as for a certain fixed value of between and , then tends to this limit on every line in , and uniformly for .

See also Vitali's Convergence Theorem


References

Titchmarsh, E. C. The Theory of Functions, 2nd ed. Oxford, England: Oxford University Press, p. 170, 1960.


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