The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Linear operators as measure preserving transformations”

Most expanding maps have no absolutely continuous invariant measure

Anthony Quas (1999)

Studia Mathematica

Similarity:

We consider the topological category of various subsets of the set of expanding maps from a manifold to itself, and show in particular that a generic C 1 expanding map of the circle has no absolutely continuous invariant probability measure. This is in contrast with the situation for C 2 or C 1 + ε expanding maps, for which it is known that there is always a unique absolutely continuous invariant probability measure.

The uniqueness of Haar measure and set theory

Piotr Zakrzewski (1997)

Colloquium Mathematicae

Similarity:

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...

On a pointwise ergodic theorem for multiparameter semigroups.

Ryotaro Sato (1994)

Publicacions Matemàtiques

Similarity:

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...

Multiparameter pointwise ergodic theorems for Markov operators on L.

Ryotaro Sato (1994)

Publicacions Matemàtiques

Similarity:

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 < ∞ the averages Anf = (n + 1)-d Σ0≤ni≤n P1

On the generalized Avez method

Antoni Leon Dawidowicz (1992)

Annales Polonici Mathematici

Similarity:

A generalization of the Avez method of construction of an invariant measure is presented.