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Cesare Arzelà

From Wikipedia, the free encyclopedia

Cesare Arzelà (1847-1912) was an Italian mathematician who taught at Bologna and is recognized for contributions in sequences of functions.

[edit] Arzela's Theorem

If $f n$ is a uniformly bounded sequence of Riemann integrable functions that converge pointwise to a Riemann integrable function $f$ on $[a, b]$ , then

$\int_{a} ^{b} f(x) dx = \lim_{n \to \infty} \int _a ^b f_n(x) dx .$

[edit] See also

Arzela-Ascoli theorem

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Categories: 1847 births | 1912 deaths | Italian mathematicians | Italy stubs | Mathematician stubs

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