Date of this Version
In this note we give a tractable necessary and sufficient condition for mutual singularity which is concerned only with the given covariance functions. The method of proof depends on a generalization, first obtained by Kraft, of a theorem of Kakutani. We give a somewhat more general version of Kraft's theorem together with a simpler proof.
Copyright 1964 National Academy of Sciences.
Shepp, L. A. (1964). The Singularity of Gaussian Measures in Function Space. PNAS, 52 (2), 430-433. Retrieved from https://repository.upenn.edu/statistics_papers/214
Date Posted: 27 November 2017
This document has been peer reviewed.