Displaying similar documents to “An equivalent measure for some nonsingular transformations and application”

On a pointwise ergodic theorem for multiparameter semigroups.

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...

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...

Genericity of nonsingular transformations with infinite ergodic index

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 G δ 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...

Exactness of skew products with expanding fibre maps

Thomas Bogenschütz, Zbigniew Kowalski (1996)

Studia Mathematica

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We give an elementary proof for the uniqueness of absolutely continuous invariant measures for expanding random dynamical systems and study their mixing properties.

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) &gt; 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...

Multiparameter pointwise ergodic theorems for Markov operators on L.

Ryotaro Sato (1994)

Publicacions Matemàtiques

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Let P1, ..., Pd be commuting Markov operators on L∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each Pi is either conservative or invertible, we prove that for every f in Lp(X,F,μ) with 1 ≤ p &lt; ∞ the averages Anf = (n + 1)-d Σ0≤ni≤n P1

Ergodic properties of skew products with Lasota-Yorke type maps in the base

Zbigniew Kowalski (1993)

Studia Mathematica

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We consider skew products T ( x , y ) = ( f ( x ) , T e ( x ) y ) preserving a measure which is absolutely continuous with respect to the product measure. Here f is a 1-sided Markov shift with a finite set of states or a Lasota-Yorke type transformation and T i , i = 1,..., max e, are nonsingular transformations of some probability space. We obtain the description of the set of eigenfunctions of the Frobenius-Perron operator for T and consequently we get the conditions ensuring the ergodicity, weak mixing and exactness of T....