Markov Uniqueness and Rademacher Theorem for Smooth Measures on an Infinite-Dimensional Space under Successful-Filtration Condition

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For a smooth measure on an infinite-dimensional space, a “successful-filtration” condition is introduced and the Markov uniqueness and Rademacher theorem for measures satisfying this condition are proved. Some sufficient conditions, such as the well-known Hoegh-Krohn condition, are also considered. Examples demonstrating connections between these conditions and applications to convex measures are given.