# Probability measures on a Polish space

Let $X$ be a Polish space, that is a separable metric complete topological space. Is the space of Borel probability measures on $X$, equipped with its weak topology, is Polish too ?

It is metric, but what about completeness and separability ?

• If probability measures means Borel probability measures then yes. This is proved e.g. in Kechris, Classical descriptive set theory, Theorem 17.23, page 112. – t.b. Jan 8 '12 at 16:27