Unformatted text preview: Z ; that is, as n → ∞ with n ∈ Nr Z . 6b: Do Billingsley’s problem, 24 . 7 P. 326. Here ( T : X, X , P ) is a mixing transformation. A fnc δ : X → [ , ∞ ) , with R X δ () d P = 1, gives rise to a new probability measure μ (the text calls it P ) by μ ( A ) := Z A δ () d P . Prove, for each measurable B , that μ ( T-n ( B )) → P ( B ) as n → ∞ . [ Hint: You might ﬁrst want to consider the case where δ is a ( scaled ) indicator function [1 / P ( A )] 1 A .]...
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- Fall '11
- Probability theory, measure, Billingsley, Prof. JLF King, ergodic theory chapter