# Giuseppe Vitali

Giuseppe Vitali
Born 26 August 1875
Ravenna, Italy
Died 29 February 1932 (aged 56)
Bologna, Italy
Nationality Italian
Fields Mathematics

Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis.

## Mathematical contributions

Vitali was the first to give an example of a non-measurable subset of real numbers, see Vitali set. His covering theorem is a fundamental result in measure theory. He also proved several theorems concerning convergence of sequences of measurable and holomorphic functions. Vitali convergence theorem generalizes Lebesgue's dominated convergence theorem. Another theorem bearing his name gives a sufficient condition for the uniform convergence of a sequence of holomorphic functions on an open domain $\emph{D} \subset \mathbb{C}$ to a holomorphic function on $\emph{D}$. This result has been generalized to normal families of meromorphic functions, holomorphic functions of several complex variables, and so on.

In the last part of his life, he also worked on absolute differential calculus and on the geometry of Hilbert spaces.[1][2]