Talk:Helly–Bray theorem

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Let P and P1, P2, ... are probability measures on some set S. Then Pn 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)

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