Here I asked the question about approximating the function $g(x) := \mathbb{E}(f(x,Y))$, where $x \in R$ and $Y$ is a random variable. If you follow the link you will see that $g(x)$ can be approximated by finite sum $\frac{1}{n}\sum_{i=1}^nf(x,\mu_i)$ with any precision we desire.

My question: whats is the speed of the convergence? Can we deduce how large $n$ should be to make error $\leq \epsilon$

Feel free to impose any reasonable conditions on $f$ and distribution of $Y$

  • $\begingroup$ Are you looking for something on the lines on concentration inequalities? $\endgroup$ – sudeep5221 Jul 6 at 13:38
  • $\begingroup$ @sudeep5221, I am looking for anything that could tell me how good my discrete approximation is $\endgroup$ – Markoff Chainz Jul 6 at 14:31

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