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.
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A. A. Dorogovtsev, “Measurable functionals and finitely absolutely continuous measures on Banach spaces,” Ukr. Mat. Zh., 52, No. 9, 1194–1204 (2000).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1367–1377, October, 2008.
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Ryabov, G.V. Finite absolute continuity of Gaussian measures on infinite-dimensional spaces. Ukr Math J 60, 1592–1604 (2008). https://doi.org/10.1007/s11253-009-0158-4
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DOI: https://doi.org/10.1007/s11253-009-0158-4