Extensions of H-Lipschitzian mappings with infinite-dimensional range

Let gamma be a Radon Gaussian measure on a locally convex space X with the Cameron-Martin space H, let A subset of X be a gamma-measurable set, and le t F: A --> E be a gamma-measurable mapping with values in a separable Hilbe rt space E such that \F(x) -F(y) \(E) less than or equal to C\x-y\(H) whene ver x, y is an element of A, x - y is an element of H. The main result in t his work gives a gamma-measurable extension of F to all of X such that \F(x + h) - F(x)\E less than or equal to C\h\(H) for all x is an element of X a nd h is an element of X. Some related results are obtained.