On positively expansive differentiable maps

Kazuhiro Sakai

Displaying similar documents to “On positively expansive differentiable maps”

Mild law of large numbers and its consequences

Jaroslav Mohapl (1993)

Mathematica Slovaca

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On pointwise ergodic theorems for positive operators

Ryotaro Sato (1990)

Studia Mathematica

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On the distribution function of the majorant of ergodic means

Lasha Epremidze (1992)

Studia Mathematica

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Let T be a measure-preserving ergodic transformation of a measure space (X,,μ) and, for f ∈ L(X), let $f * = s u p_{N} 1 / N \sum_{m = 0}^{N - 1} f \circ T^{m}$ . In this paper we mainly investigate the question of whether (i) $ʃ_{a}^{\infty} | μ (f * > t) - 1 / t ʃ_{(f * > t)} f d μ | d t < \infty$ and whether (ii) $ʃ_{a}^{\infty} | μ (f * > t) - 1 / t ʃ_{(f > t)} f d μ | d t < \infty$ 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 $f \circ T^{m}$ are independent. Related inequalities are proved. Some examples and counterexamples are constructed. Several known results are obtained as corollaries. ...

Metric properties of alternating Lüroth series

Kalpazidou, Sofia, Knopfmacher, Arnold, Knopfmacher, John (1991)

Portugaliae mathematica

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An atomic theory of ergodic $H^{p}$ spaces

R. Caballero, A. de la Torre (1985)

Studia Mathematica

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A general ratio ergodic theorem for Abel sums

Ryotaro Sato (1973)

Studia Mathematica

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On the pointwise ergodic theorems in $L_{p}$ (1

R. Emilion (1985)

Studia Mathematica

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On the ratio maximal functions for an ergodic flow

Ryotaro Sato (1984)

Studia Mathematica

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Convergence of the averages and finiteness of ergodic power funtions in weighted L spaces.

Pedro Ortega Salvador (1991)

Publicacions Matemàtiques

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Let (X, F, μ) be a finite measure space. Let T: X → X be a measure preserving transformation and let Af denote the average of Tf, k = 0, ..., n. Given a real positive function v on X, we prove that {Af} converges in the a.e. sense for every f in L(v dμ) if and only if inf v(Tx) > 0 a.e., and the same condition is equivalent to the finiteness of a related ergodic power function Pf for every f in L(v dμ). We apply this result to characterize, being T null-preserving, the finite...