Characteristic Functional of a Probability Measure Absolutely Continuous with Respect to a Gaussian Radon Measure
Abstract
Let mu and mu sub 1 be probability measures on a locally convex Hausdorff real topological linear space E. C.R. Baker posed the problem of characterizing the absolute continuity of mu and mu sub 1 by their characteristic functionals. The aim of this paper is to give an answer to this problem in the case where mu is a Gaussian Radon measure. We shall define a Fourier transform, establish the inversion formula, and then give a necessary and sufficient condition for mu sub 1 to be absolutely continuous with respect to mu based on the characteristic functional. As applications, for the convolution mu sub 1 = mu* v, where v is a Radon measure on E, we shall give some concrete sufficient conditions on v for mu* v << mu.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1984
- Accession Number
- ADA149482
Entities
People
- Hiroshi Sato
Organizations
- University of North Carolina at Chapel Hill