On a Laplace transform based metric for probabilities on a Hilbert space

Let D be a closed subset of a real separable Hilbert space H. Let;M(D) deno te the set of all Borel probability measures on D and L(D) thr set of all p robabilities with integrable Laplace transform. A metric d, based on the La place transform, is defined on L(D). Topological properties, viz., separabi lity, connectedness, completeness, compactness and local compactness. of (L (D), ci) are investigated, and the d-topology is compared with the topology of weak convergence.