# Accession Number:

## ADA149482

# Title:

## Characteristic Functional of a Probability Measure Absolutely Continuous with Respect to a Gaussian Radon Measure

# Descriptive Note:

## Technical rept.

# Corporate Author:

## NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1984-08-01

# Pagination or Media Count:

## 33.0

# 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.

# Descriptors:

# Subject Categories:

- Statistics and Probability