Abstract
Let T be any measure preserving transformation acting on the sample space Ω and let ξ = ξ(ω), ω ∈ Ω, be any random variable, chosen so that the expected value Eξ(ω) exists. Prove that Eξ(ω) =Eξ(Tω).
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Notes
- 1.
It is assumed throughout the entire chapter that the probability space \((\Omega,\mathcal{F},\mathsf{P})\) is complete.
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© 2012 Springer Science+Business Media, LLC
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Shiryaev, A.N. (2012). Stationary (in Strict Sense) Random Sequences and Ergodic Theory. In: Problems in Probability. Problem Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3688-1_5
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DOI: https://doi.org/10.1007/978-1-4614-3688-1_5
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