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Markov Chains by J. R. Norris

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6Appendix: probability and measure

Section 6.1 contains some reminders about countable sets and the discrete version of measure theory. For much of the book we can do without explicit mention of more general aspects of measure theory, except an elementary understanding of Riemann integration or Lebesgue measure. This is because the state-space is at worst countable. The proofs we have given may be read on two levels, with or without a measure-theoretic background. When interpreted in terms of measure theory, the proofs are intended to be rigorous. The basic framework of measure and probability is reviewed in Sections 6.2 and 6.3. Two important results of measure theory, the monotone convergence theorem and Fubini’s theorem, are needed a number ...

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