**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.