Cesare Arzelà

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Cesare Arzelà (6 March 1847, Santo Stefano di Magra, La Spezia – 15 March 1912, Santo Stefano di Magra) was an Italian mathematician who taught at Bologna and is recognized for contributions in sequences of functions.

[edit] Life

He was a pupil of the School Norm. of Pisa where he graduated in 1869. Arzela came from a poor household; therefore he couldn't start his study until 1871, when he studied in Pisa under Enrico Betti and Ulisse Dini.

He was working in Florence (from 1875) and in 1878 obtained the Chair of Algebra at the University of Palermo.

After that he became a professor in 1880 at the University of Bologna at the department of analysis. He conducted research in the field of functional theory. His most famous student was Leonida Tonelli.

In 1889 he generalized the Ascoli theorem to Arzelà–Ascoli theorem, an important theorem in functional theory.

He was a member of Nat. dei Lincei, and several other academies.

[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

^{[citation needed]}

[edit] External links

• Cesare Arzelà at the Mathematics Genealogy Project

Persondata
NAME	Cesare Arzelà
ALTERNATIVE NAMES
SHORT DESCRIPTION
DATE OF BIRTH	6 March 1847
PLACE OF BIRTH	Santo Stefano di Magra, La Spezia, Italy
DATE OF DEATH	15 March 1912
PLACE OF DEATH	Santo Stefano di Magra

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