Continuity of Measureson Hilbert Space
نویسنده
چکیده
The paper considers continuity properties of a nite Borel measure on a separable Hilbert space X. Continuity of the mappings x 7 ! (A + x) on a subspace H, uniformly in A 2 B(X), is characterized by the existence of a nonstandard density of having a certain property. This generalizes a well known standard result for measures on R n. The ideas are illustrated with reference to Gaussian measures and an application to statistical solutions of the heat equation is given. 1. Introduction. This paper is concerned with various concepts of continuity of a nite Borel measure on a separable Hilbert space X, in the sense of continuity of the mappings x 7 ! (A + x) for A 2 B(X). A rst result
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