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Unformatted text preview: Z ; that is, as n with n Nr Z . 6b: Do Billingsleys problem, 24 . 7 P. 326. Here ( T : X, X , P ) is a mixing transformation. A fnc : X [ , ) , with R X () d P = 1, gives rise to a new probability measure (the text calls it P ) by ( A ) := Z A () d P . Prove, for each measurable B , that ( T-n ( B )) P ( B ) as n . [ Hint: You might rst want to consider the case where is a ( scaled ) indicator function [1 / P ( A )] 1 A .]...
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