Gaussian Measure on a Banach Space and Abstract Winer Measure
- 1 November 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 36, 65-81
- https://doi.org/10.1017/s002776300001312x
Abstract
In this paper, we shall show that any Gaussian measure on a separable or reflexive Banach space is an abstract Wiener measure in the sense of L. Gross [1] and, for the proof of that, establish the Radon extensibility of a Gaussian measure on such a Banach space. In addition, we shall give some remarks on the support of an abstract Wiener measure.Keywords
This publication has 7 references indexed in Scilit:
- Potential theory on Hilbert spaceJournal of Functional Analysis, 1967
- Measures on infinite dimensional vector spacesPublications of the Research Institute for Mathematical Sciences, 1965
- Measurable functions on Hilbert spaceTransactions of the American Mathematical Society, 1962
- Distributions in Hilbert space and canonical systems of operatorsTransactions of the American Mathematical Society, 1958
- A Remark on Characteristic FunctionalsTheory of Probability and Its Applications, 1958
- On characteristic functions of Banach space valued random variablesPacific Journal of Mathematics, 1957
- Tensor algebras over Hilbert spaces. ITransactions of the American Mathematical Society, 1956