The Singularity of Gaussian Measures in Function Space

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Statistics and Probability
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Shepp, Larry A
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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.

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1964-08-15
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PNAS
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