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Dini theorem

From Encyclopedia of Mathematics
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on uniform convergence

If the functions , are continuous and non-negative on a segment and if the sum of the series is a continuous function on this segment, then the series converges uniformly on . Dini's theorem can be generalized to the case when an arbitrary compactum is the domain of definition of the functions .

How to Cite This Entry:
Dini theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dini_theorem&oldid=32779
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article