The purpose of this paper is to extend 
Prokhorov-LeCam's criteria for compactness 
and Varadarajan's criterion for metrizability
to vector measures with values in certain 
locally convex spaces.
Our results contain not only Prokhorov-LeCam's 
and Varadarajan's criteria for real measures 
but a sequential compactness criterion which 
was recently given by M\"{a}rz and Shortt for 
vector measures with values in a Banach space.