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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.
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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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