Existence and convergence of probability measures in Banach spaces.

de Acosta, Alejandro D.

doi:10.1090/S0002-9947-1970-0267614-9

Existence and convergence of probability measures in Banach spaces.
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by Alejandro D. de Acosta PDF

Trans. Amer. Math. Soc. 152 (1970), 273-298 Request permission

Abstract:

Theorems of the Bochner-Sazonov type are proved for Banach spaces with a basis. These theorems give sufficient conditions of a topological nature under which a positive definite function is the characteristic functional of a probability measure. The conditions are, in a certain natural sense, best possible. Central limit theorems of the Lindeberg type for triangular systems of random variables taking values in a Banach space with a basis are obtained. Applications to ${l_p}$ and $C[0,1]$ are given.

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