Vol. 52, No. 2, 1974

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Absolute continuity for abstract Wiener spaces

Tyrone Duncan

Vol. 52 (1974), No. 2, 359–367

Certain smooth homeomorphisms on an abstract Wiener space are shown to induce a measure that is absolutely continuous with respect to an abstract Wiener measure which is the measure determined on a Banach space from the canonical normal distribution on a Hilbert space by the completion of the Hilbert space with respect to a measurable seminorm. The notion of an abstract Wiener space is an abstraction of one technique to show the countable additivity for Wiener measure, the measure for Brownian motion. The generalizations of absolute continuity obtained here reduce exactly to the well known results for absolute continuity for Gaussian measures.

Mathematical Subject Classification 2000
Primary: 60G30
Secondary: 28A40
Received: 23 March 1973
Revised: 8 March 1974
Published: 1 June 1974
Tyrone Duncan
University of Kansas
United States