Let be an analytic function of , regular in the half-strip defined by and . If is bounded 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 .

**References**

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

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1999-05-26