(Vague precompactness of s.p.m.) For
of s.p.m. there is a subsequence
that converges vaguely to a s.p.m.
by a sequence of piecewise constant function. For the piecewise functions the
statement is apparent. This argument works in both directions.
(Tight sequence). The sequence of measures
is called "tight"
(Precompactness of a
tight sequence of p.m.). Let
be a tight sequence of p.m. The there is a subsequence that converges vaguely
to a p.m..