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On Abstract Wiener Measure*

Published online by Cambridge University Press:  22 January 2016

Balram S. Rajput
Balram S. Rajput*
Affiliation:
Departments of Mathematics and Statistics, University of North Carolina, Chapel Hill, N.C. 27514
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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 .

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 46 , March 1972 , pp. 155 - 160
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

Footnotes

*

This research was partially supported by the NSF under Grant GU-2059.

References

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[6] Sato, H., Gaussian measure on a Banach space and abstract Wiener measure, Nagoya Math. J., 36 (1969), pp. 65–81.Google Scholar