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

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 $*$, then

$\backslash int\_\{a\}\; ^\{b\}\; f(x)\; dx\; =\; \backslash lim\_\{n\; \backslash to\; \backslash infty\}\; \backslash int\; \_a\; ^b\; f\_n(x)\; dx\; .$

See also

• Arzela-Ascoli theorem

1847 births | 1912 deaths | Italian mathematicians

Cesare Arzelà | Cesare Arzelà