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Displaying similar documents to “On the sequence of integer parts of a good sequence for the ergodic theorem”

Pointwise ergodic theorems in Lorentz spaces L(p,q) for null preserving transformations

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 n - 1 ∑ i = 0 n - 1 f ∘ τ i ( x ) converges almost everywhere to a function f* in L ( p 1 , q 1 ] , where (pq) and ( p 1 , q 1 ] are assumed to be in the set ( r , s ) : r = s = 1 , o r 1 < r < ∞ a n d 1 ≤ s ≤ ∞ , o r r = s = ∞ . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...

Hopf's ratio ergodic theorem by inducing

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.