A zero-one law for Gaussian processes

Author:
Naresh C. Jain

Journal:
Proc. Amer. Math. Soc. **29** (1971), 585-587

MSC:
Primary 60.40

MathSciNet review:
0278369

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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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DOI:
http://dx.doi.org/10.1090/S0002-9939-1971-0278369-2

Keywords:
Gaussian process,
zero-one law

Article copyright:
© Copyright 1971
American Mathematical Society