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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Existence and convergence of probability measures in Banach spaces.

Author: Alejandro D. de Acosta
Journal: Trans. Amer. Math. Soc. 152 (1970), 273-298
MSC: Primary 60.08
MathSciNet review: 0267614
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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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Keywords: Characteristic functional, Bochner theorem in Banach space, tightness, weak convergence of probability measures, central limit theorem in Banach space
Article copyright: © Copyright 1970 American Mathematical Society

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