Sequential Compactness for the Weak Topology of Vector Measures in Certain Nuclear Spaces

Abstract We give a sequential compactness criterion for the weak topology of vector measures with values in certain nuclear spaces, such as the space S of all rapidly decreasing, infinitely differentiable functions, the space D of all test functions, and the strong duals of those spaces. This result contains Prokhorov–LeCam's criterion for real measures and applies to cases which are not covered by März–Shortt's criterion for Banach space valued vector measures.