Functions of bounded variation in Hilbert spaces endowed with a Gaussian measure γ are studied, mainly in connection with Ornstein-Uhlenbeck semigroups for which γ is invariant.
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Luigi Ambrosio, Giuseppe Da Prato, Diego Pallara, BV functions in a Hilbert space with respect to a Gaussian measure. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 4, pp. 405–414DOI 10.4171/RLM/580