Displaying similar documents to “Some fine properties of sets with finite perimeter in Wiener spaces”

Compactness of the integration operator associated with a vector measure

S. Okada, W. J. Ricker, L. Rodríguez-Piazza (2002)

Studia Mathematica

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A characterization is given of those Banach-space-valued vector measures m with finite variation whose associated integration operator Iₘ: f ↦ ∫fdm is compact as a linear map from L¹(m) into the Banach space. Moreover, in every infinite-dimensional Banach space there exist nontrivial vector measures m (with finite variation) such that Iₘ is compact, and other m (still with finite variation) such that Iₘ is not compact. If m has infinite variation, then Iₘ is never compact.

On Gaussian Brunn-Minkowski inequalities

Franck Barthe, Nolwen Huet (2009)

Studia Mathematica

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We are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrhard inequality for m Borel or convex sets based on a previous work by Borell. Our method also yields semigroup proofs of the geometric Brascamp-Lieb inequality and of its reverse form, which follow exactly the same lines.

Some Fine Properties of BV Functions on Wiener Spaces

Luigi Ambrosio, Michele Miranda Jr., Diego Pallara (2015)

Analysis and Geometry in Metric Spaces

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In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux. ...