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单词 WeierstrassMtestForContinuousFunctions
释义

Weierstrass M-test for continuous functions


When the set X in the statement of the Weierstrass M-testMathworldPlanetmathPlanetmath is a topological spaceMathworldPlanetmath, a strengthening of the hypothesis produces a stronger result. When the functions fn are continuousMathworldPlanetmath, then the limit of the series f=n=1fn is also continuous.

The proof follows directly from the fact that the limit of a uniformly convergent sequence of continuous functions is continuous.

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更新时间:2025/5/5 1:35:50