Quadratic zero-one laws for Gaussian measures and the distribution of quadratic forms

de Acosta, Alejandro

doi:10.1090/S0002-9939-1976-0405524-5

Quadratic zero-one laws for Gaussian measures and the distribution of quadratic forms
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by Alejandro de Acosta PDF

Proc. Amer. Math. Soc. 54 (1976), 319-325 Request permission

Erratum: Proc. Amer. Math. Soc. 61 (1976), 187.

Abstract:

Given a centered Gaussian measure on a vector space, the set of points where a sequence of quadratic forms converges to a constant has probability zero or one. The distribution of a quadratic form under a Gaussian measure is either point mass at zero or absolutely continuous.

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