On the ergodic theorems (II) (Ergodic theory of continued fractions)
C. Ryll-Nardzewski (1951)
Studia Mathematica
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C. Ryll-Nardzewski (1951)
Studia Mathematica
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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...
I. Assam, J. Woś (1990)
Studia Mathematica
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Idris Assani, Zoltán Buczolich, Daniel R. Mauldin (2004)
Acta Universitatis Carolinae. Mathematica et Physica
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Ryotaro Sato (1977)
Commentationes Mathematicae Universitatis Carolinae
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Ryotaro Sato (1980)
Studia Mathematica
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Dalibor Volný (1989)
Aplikace matematiky
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The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.
Mercer, A.McD. (1993)
International Journal of Mathematics and Mathematical Sciences
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