On the extension of cylinder measures to $\tau$-smooth measures in linear spaces

Abstract:

We give a necessary and sufficient condition for a cylindrical probability measure in the weak$^{\ast }$-dual of an arbitrary l.c.s. to extend to a $\tau$-smooth Borel-measure; this is to a certain extent a “$\tau$-smooth analogue” of the well-known Prohorov extension theorem (cf. [8, Lemma 3]). Finally, we give two examples marking off our result from related ones treated in the literature.