An algebraic formulation of ergodic problems
An algevraic study of the Kolmogorov entropy
An Alpern tower independent of a given partition
Given a measure-preserving transformation T of a probability space (X,ℬ,μ) and a finite measurable partition ℙ of X, we show how to construct an Alpern tower of any height whose base is independent of the partition ℙ. That is, given N ∈ ℕ, there exists a Rokhlin tower of height N, with base B and error set E, such that B is independent of ℙ, and TE ⊂ B.
An alternative proof of the uniqueness of martingale-coboundary decomposition of strictly stationary processes
P. Samek and D. Volný, in the paper ``Uniqueness of a martingale-coboundary decomposition of a stationary processes" (1992), showed the uniqueness of martingale-coboundary decomposition of strictly stationary processes. The original proof is given by reducing the problem to the ergodic case. In this note we give another proof without such reduction.
An analog of the Marcinkiewicz integral in ergodic theory
An anti-classification theorem for ergodic measure preserving transformations
Despite many notable advances the general problem of classifying ergodic measure preserving transformations (MPT) has remained wide open. We show that the action of the whole group of MPT’s on ergodic actions by conjugation is turbulent in the sense of G. Hjorth. The type of classifications ruled out by this property include countable algebraic objects such as those that occur in the Halmos–von Neumann theorem classifying ergodic MPT’s with pure point spectrum. We treat both the classical case of...
An atomic theory of ergodic spaces
An Elementary Lemma on Sequences of Integers and Its Apllications to Functional Analysis.
An equivalent measure for some nonsingular transformations and application
An example concerning automorphisms of generalized cubes
An example of a weak Bernoulli process which is not finitary
An exponential estimate for convolution powers
We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.
An extension which is relatively twofold mixing but not threefold mixing
We give an example of a dynamical system which is mixing relative to one of its factors, but for which relative mixing of order three does not hold.
Analytic nonregular cocycles over irrational rotations
Analytic cocycles of type over an irrational rotation are constructed and an example of that type is given, where all corresponding special flows are weakly mixing.
Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios
Using the ratio ergodic theorem for a measure preserving transformation in a -finite measure space we give a straightforward proof of Derriennic’s reverse maximal inequality for the supremum of ergodic ratios.
Appendix on return-time sequences
Applications des propriétés de moyenne d'un groupe localement compact à la théorie ergodique
Approximation for the invariant measures of Markov maps in Rd.
Approximation of homogeneous measures in the 2-Wasserstein metric.
Approximation of -processes by Gaussian processes.