|ISSN 1088-6826(online) ISSN 0002-9939(print)|
A zero-one law for Gaussian processes
Abstract: Let be a Gaussian probability measure on the measurable space , where X is a linear space of realvalued functions over a complete separable metric space T, and is the -algebra generated by sets of the form being the Borel sets of . The covariance is assumed continuous on . If G is a subgroup of X and belongs to the -algebra (the completion of with respect to ), then it is shown that or 1.
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