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Transactions of the American Mathematical Society
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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DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0267614-9
PII: S 0002-9947(1970)0267614-9
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