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Some Results on Convergence Rates for Weighted Averages
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a-algebra a-finite invariant measure admits an approximation algebra approximation with speed assume automorphism Bernoulli shift bounded Chacon condition construction contains countable define definition denote derivation basis differential equations disjoint entropy ergodic automorphism ergodic theory exists finite measure finitely determined flow built functions f hence implies integer Ionescu Tulcea isomorphism LA,n Large Numbers Law of Large Lebesgue measure Lemma lifting lower density mapping Markov martingales Math measure preserving transformation measure space metric space nonsingular null set obtain operator partition positive integer positive measure positive numbers probability measure probability space proof of theorem properties Proposition prove Random Variables real numbers restricted result satisfying Seiten semigroup set of sequences strictly ergodic strictly invariant null strongly generating set subset T-invariant time-L topology Tulcea wandering set weak Bernoulli weakly equivalent