On Subgradients of a Convex Function in Abstract Wiener Space

摘要

An abstract Wiener space (S, beta) is defined such that S is a real, locally convex Hausdorff vector space and beta a fixed centered Gaussian Radon measure on S. The main result shows that any convex function f's tends to R cup braces + infinity braces being bounded above on a set of positive beta measure, has a beta measurable subgradient at each point in the set ri sub beta braces f + infinity braces.