Before revision: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm  )}(}{\cal  {\cal   function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).
After revision: The Markov-Chain Monte-Carlo (MCMC) method has been used widely in the literature for various applications, in particular estimating the expectation \mathbb{E_{\pi}[f] of a } {\rm )}(}{\cal ,f), which depends on a Markov chain{\cal function f: \Omega \to [a,b] over a distribution \pi on \Omega (a. k.a . mean-estimation), to within \varepsilon additive error (w.h.p.).