Sublinear functionals ergodicity and finite invariant measures.
Das, G., Patel, B.K. (1989)
International Journal of Mathematics and Mathematical Sciences
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Das, G., Patel, B.K. (1989)
International Journal of Mathematics and Mathematical Sciences
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F. Martín-Reyes, A. de la Torre (1994)
Studia Mathematica
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Antoni Leon Dawidowicz (1992)
Annales Polonici Mathematici
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A generalization of the Avez method of construction of an invariant measure is presented.
Piotr Zakrzewski (1997)
Colloquium Mathematicae
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Let G be a group of homeomorphisms of a nondiscrete, locally compact, σ-compact topological space X and suppose that a Haar measure on X exists: a regular Borel measure μ, positive on nonempty open sets, finite on compact sets and invariant under the homeomorphisms from G. Under some mild assumptions on G and X we prove that the measure completion of μ is the unique, up to a constant factor, nonzero, σ-finite, G-invariant measure defined on its domain iff μ is ergodic and the G-orbits...
Jacek Cichoń, Przemyslaw Szczepaniak (2001)
Acta Universitatis Carolinae. Mathematica et Physica
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A. B. Kharazishvili (2010)
Acta Universitatis Carolinae. Mathematica et Physica
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C. Ryll-Nardzewski (1954)
Studia Mathematica
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Antoni Leon Dawidowicz (1989)
Annales Polonici Mathematici
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Ryotaro Sato (1994)
Publicacions Matemàtiques
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Let Ti (i = 1, 2, ..., d) be commuting null preserving transformations on a finite measure space (X, F, μ) and let 1 ≤ p < ∞. In this paper we prove that for every f ∈ Lp(μ) the averages Anf(x) = (n + 1)-d Σ0≤ni≤n f(T1 n1 T2 n2...