Dini theorem
From Encyclopedia of Mathematics
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
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