Second derivatives of convex functions in the sense of A.\ D.\ Aleksandrov on infinite-dimensional spaces with measure

DOI10.1007/s11006-006-0052-4zbMath1121.46061OpenAlexW2002117635WikidataQ112879548 ScholiaQ112879548MaRDI QIDQ881023

Vladimir I. Bogachev, Beniamin Goldys

Publication date: 21 May 2007

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11006-006-0052-4

zbMATH Keywords

convex functionBorel measureRadon measureGaussian measuresecond derivativedifferentiable measureSkorokhod derivative

Mathematics Subject Classification ID

Continuous and differentiable maps in nonlinear functional analysis (46T20) Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds (46T12)

Related Items (2)

Second order derivative of a functional associated to an optimal transport map ⋮ On the fluctuations about the Vlasov limit for \(N\)-particle systems with mean-field interactions

Cites Work

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• Differentiable measures and the Malliavin calculus
• On the integrability of logarithmic derivatives of measures.
• The notion of convexity and concavity on Wiener space
• A highly non-smooth norm on Hilbert space
• Some remarks on Rademacher's theorem in infinite dimensions
• Second Order Differentiability of Convex Functions in Banach Spaces
• Second order differentiability and Lipschitz smooth points of convex functionals
• ON THE MONGE–AMPÈRE EQUATION IN INFINITE DIMENSIONS

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