Can anyone say how to relate Stone-Weierstrass approximation theorem in this problem? Given that $\mu$ and $\nu$ are two probability measure on the real line, if for all bounded continuous functions $f$, $\int f d \mu = \int f d \nu$, then $\mu=\nu$?
Prove: If $\int f d\mu = \int f d \nu$ for all $f$, then $\mu = \nu$
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6elinor, I _strongly encourage you_ to start accepting answers to your questions. This is a basic courtesy to show that you appreciate the work they've done, for free, to assist you, a total stranger. – 2011-03-07