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Baris 165:
can be made minimal ''independently'' of ''x'' by choosing a sufficiently large ''N''.
Uniform convergence is desirable for a series because many properties of the terms of the series are then retained by the limit. For example, if a series of continuous functions converges uniformly, then the limit function is also continuous. Similarly, if the ''ƒ''<sub>''n''</sub> are [[integral|integrable]] on a closed and bounded interval ''I'' and converge uniformly, then the series is also integrable on ''I'' and can be integrated term-by-term. Tests for uniform convergence include the [[Weierstrass M-test|Weierstrass' M-test]], [[Abel's uniform convergence test]], [[Dini's test]]--><!--
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More sophisticated types of convergence of a series of functions can also be defined. In [[measure theory]], for instance, a series of functions converges [[almost everywhere]] if it converges pointwise except on a certain set of [[null set|measure zero]]. Other [[modes of convergence]] depend on a different [[metric space]] structure on the space of functions under consideration. For instance, a series of functions '''converges in mean''' on a set ''E'' to a limit function ''ƒ'' provided
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