Cesare Arzel

=Cesare Arzel= (1847-1912) Italian analyst, taught at Bologna and is recognized for contributions in sequences of functions.

Arzela's Theorem

If {a_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 .

 

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