Giuseppe Vitali - Mathematical Contributions

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 ⊂ℂ to a holomorphic function on This result has been generalized to normal families of meromorphic functions, holomorphic functions of several complex variables, and so on.