Markov Chains: Analytic and Monte Carlo Computations

A.3 Measure-theoretic framework

This appendix introduces without proofs the main notions and results in measure and integration theory, which allow to treat the subject of Markov chains in a mathematically rigorous way.

A.3.1 Probability spaces

A probability space is given by

1. a set encoding all possible random outcomes,
2. a -field , which is a set constituted of certain subsets of , and satisfies
   • the set is in ,
   • if is in , then its complement is in ,
   • if for in is in , then is in ,
3. a probability ...