On some Markov matrices arising from the generalized Collatz mapping
R. Buttsworth, K. Matthews (1990)
Acta Arithmetica
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R. Buttsworth, K. Matthews (1990)
Acta Arithmetica
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K. Matthews, A. Watts (1985)
Acta Arithmetica
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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Ryotaro Sato (1995)
Studia Mathematica
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Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average converges almost everywhere to a function f* in , where (pq) and are assumed to be in the set . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...
Janusz Woś (1987)
Colloquium Mathematicae
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Roland Zweimüller (2004)
Colloquium Mathematicae
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We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.
Paweł Głowacki (1981)
Studia Mathematica
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Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)
Studia Mathematica
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We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.
J. Choksi, M. Nadkarni (2000)
Colloquium Mathematicae
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It is shown that in the group of invertible measurable nonsingular transformations on a Lebesgue probability space, endowed with the coarse topology, the transformations with infinite ergodic index are generic; they actually form a dense set. (A transformation has infinite ergodic index if all its finite Cartesian powers are ergodic.) This answers a question asked by C. Silva. A similar result was proved by U. Sachdeva in 1971, for the group of transformations preserving an infinite...
R. Sato (1990)
Colloquium Mathematicae
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