Abstract: Let be a probability space. denotes a metric space, and
stands for the -field generated by open sets of The set is assumed to be a
separable and complete space. A sequence of random elements,
defined on a probability space taking values in is called if
for every with there exists a probability measure such
that

There are given conditions concerning the set of probability
measures, under which there exists a random element such that the sequence
of random elements converges in probability to