On the distribution function of the majorant of ergodic means

• Autorzy: Lasha Epremidze
• Języki publikacji: EN

Abstrakty

EN

Let T be a measure-preserving ergodic transformation of a measure space (X,𝕊,μ) and, for f ∈ L(X), let $f* = sup_N {1/N} ∑_{m=0}^{N - 1} f ∘ T^m$. In this paper we mainly investigate the question of whether (i) $ʃ_a^∞ |μ(f*>t) - {1/t} ʃ_{(f*>t)} fdμ|dt < ∞$ and whether (ii) $ʃ_a^∞ |μ(f*>t) - {1/t} ʃ_{(f>t)} fdμ|dt < ∞$ for some a > 0. It is proved that (i) holds for every f ≥ 0. (ii) holds if f ≥ 0 and f log log (f + 3) ∈ L(X) or if μ(X) = 1 and the random variables $f ∘ T^m$ are independent. Related inequalities are proved. Some examples and counterexamples are constructed. Several known results are obtained as corollaries.

Kategorie tematyczne

• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 103
• Numer: 1
• Strony: 1-15

Daty

wydano

1992

otrzymano

1989-07-19

poprawiono

1991-07-05

Twórcy

autor

Lasha Epremidze

• A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Rukhadze 1, 380093 Tbilisi, Georgia

Bibliografia

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