Birkhoff's ergodic theorem and the maximal ergodic theorem
نویسندگان
چکیده
منابع مشابه
Easy and nearly simultaneous proofs of the Ergodic Theorem and Maximal Ergodic Theorem
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem. Let (X,B, μ) be a probability space, T : X → X a (possibly noninvertible) measurepreserving transformation, and f ∈ L(X,B, μ). Let
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Measure-preserving systems arise in a variety of contexts, such as probability theory, information theory, and of course in the study of dynamical systems. However, ergodic theory originated from statistical mechanics. In this setting, T represents the evolution of the system through time. Given a measurable function f : X → R, the series of values f(x), f(Tx), f(T x)... are the values of a phy...
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Michael Lavine Duke University, Durham, NC, USA. Summary. In recent years there have been several papers giving examples of Markov Chain Monte Carlo (MCMC) algorithms whose invariant measures are improper (have infinite mass) and which therefore are not positive recurrent, yet which have subchains from which valid inference can be derived. These are nonergodic (not having a limiting distributio...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1939
ISSN: 0386-2194
DOI: 10.3792/pia/1195579375