2017
Том 69
№ 9

All Issues

Finite absolute continuity of Gaussian measures on infinite-dimensional spaces

Ryabov G. V.

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Abstract

We study the notion of finite absolute continuity for measures on infinite-dimensional spaces. For Gaussian product measures on \(\mathbb{R}^{\infty}\) and Gaussian measures on a Hilbert space, we establish criteria for finite absolute continuity. We consider cases where the condition of finite absolute continuity of Gaussian measures is equivalent to the condition of their equivalence.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 10, pp 1592-1604.

Citation Example: Ryabov G. V. Finite absolute continuity of Gaussian measures on infinite-dimensional spaces // Ukr. Mat. Zh. - 2008. - 60, № 10. - pp. 1367–1377.

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