On Abstract Wiener Measure*
- 1 March 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 46, 155-160
- https://doi.org/10.1017/s0027763000014835
Abstract
In a recent paper, Sato [6] has shown that for every Gaussian measure n on a real separable or reflexive Banach space (X, ‖ • ‖) there exists a separable closed sub-space X〵 of X such that and is the σ-extension of the canonical Gaussian cylinder measure of a real separable Hilbert space such that the norm is contiunous on and is dense in The main purpose of this note is to prove that ‖ • ‖ x〵 is measurable (and not merely continuous) on .Keywords
This publication has 4 references indexed in Scilit:
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- Measurable functions on Hilbert spaceTransactions of the American Mathematical Society, 1962
- Integration and nonlinear transformations in Hilbert spaceTransactions of the American Mathematical Society, 1960
- The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalitiesProceedings of the American Mathematical Society, 1955