Shepp, Larry A2023-05-232023-05-231964-08-152016-08-12https://repository.upenn.edu/handle/20.500.14332/47576In 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.Statistics and ProbabilityArticle