Talk:Helly–Bray theorem

Let P and P₁, P₂, ... are probability measures on some set S. Then P_n converges weakly to P if and only if

$\int _{S}g\,dP_{n}\rightarrow \int _{S}g\,dP,\quad n\rightarrow \infty ,$

for all bounded, continuous and real-valued functions on S.

I am puzzled by the above. In order that a function be continuous on S, there must be some topology on S. Is S supposed to be some subset of the real line, or what? Michael Hardy 22:34, 9 July 2005 (UTC)