Cesare Arzelà (1847-1912) was an Italianmathematician who taught at Bologna and is recognized for contributions in sequences of functions. A mathematician is a person whose area of study and research is mathematics. ... Bologna (from Latin Bononia, Bulaggna in the local dialect) is the capital city of Emilia-Romagna in northern Italy, between the Po River and the Apennines. ...
Arzela's Theorem
If an is a uniformly bounded sequence of Riemann integrable functions that converge pointwise to a Riemann integrable function f on [a,b], then
Here, C(X, Y) denotes the set of all continuous functions from X to Y, and a subset F is pointwise relatively compact iff for all x in X, the set {f(x) : f in F} is relatively compact in Y.
The name comes about as this is a generalization going back to CesareArzelà of Ascoli's theorem.
This article incorporates material from Ascoli-Arzelà theorem on PlanetMath, which is licensed under the GFDL.
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