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- W2059646522 abstract "implies (2) for r = 1. Condition (1) is clearly necessary when r > 1 and, as has been demons t r a t ed b y BV~XHOLDER [1], (3) is likewise necessary for (2) when r = 1. Here , i t will be shown for i . i .d. {Xn, n ~ 1} with E X n = 0 t h a t for r > 2, the n X same hypothes is (1) implies E s u p c n ] S n ] r 1, with ~ > 0 and k ---grea tes t integer 2 under the s t ipula ted conditions, Ect l St I r 2 and r = 2 follow directly, rests upon the classical result of WIENER cited above." @default.
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- W2059646522 date "1967-01-01" @default.
- W2059646522 modified "2023-10-16" @default.
- W2059646522 title "A dominated ergodic type theorem" @default.
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- W2059646522 doi "https://doi.org/10.1007/bf00536913" @default.
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