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Basic inequalities and limit theorems
General invariance theorems
5 other sections not shown
absolutely regular sequence arbitrary assume asymptotic B-valued random elements Banach space bounded choose coefficient compact completely conditions of Theorem consider continuous converges corresponding covariance defined definition denotes dependent differentiable distribution function easily estimate exists expansion finite fixed following conditions following lemma following theorem Gaussian given Hence holds implies independent inequality kernel Lemma limit log log mean measurable method mixing sequence normal obtain obvious positive integer positive numbers probability space proof of Theorem prove random variables random vectors relations Remark replacement respectively result sampling satisfied sequence of random stationary absolutely regular stationary sequence statistics strong mixing subsets sufficiently large sums Suppose conditions tends U-statistics uniformly values weakly X-valued random Yoshihara zero