J. Kawabe

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 $\mathscr S$ of all rapidly decreasing, infinitely differentiable functions, the space $\mathscr D$ 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 M\"{a}rz-Shortt's criterion for Banach space valued vector measures.