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Gaussian measures in
function space
Lawrence A. Shepp |
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Vol. 17 (1966), No. 1, 167–173
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Abstract |
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Two Gaussian measures are either mutually singular or equivalent. This dichotomy was first discovered by Feldman and Hajek (independently). We give a simple, almost formal, proof of this result, based on the study of a certain pair of functionals of the two measures. In addition we show that two Gaussian measures with zero means and smooth Polya-type covariances (on an interval) are equivalent if and only if the right-hand slopes of the covariances at zero are equal. |
Mathematical Subject Classification
Primary: 60.40
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Milestones
Received: 6 October 1964
Revised: 20 November 1964
Published: 1 April 1966
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Authors |
| Lawrence A. Shepp | |
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