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Post Undeleted by Mark Meckes
2 deleted 178 characters in body

I assume you meant $\frac{1}{n}\sum_{t=1}^n f(X_t)$ converges to $\mathrm{E}_\pi (f)$. I'll also quibble and point out that the (classical) CLT doesn't give error rates in terms of n, but the Berry-Esseen theorem does.