On invariant functions for positive operators
On invariant measures for piecewise -transformations of the n-dimensional cube
On invariant measures for piecewise convex transformations
On invariant measures for some infinite-dimensional dynamical systems
On mappings isomorphic to r-adic transformations
On Marginal Distributions and Isomorphisms of Stationary Processes.
On metric isomorphism of Morse dynamical systems
On metric properties of substitutions
On mixing transformations.
On non-ergodic versions of limit theorems
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.
On nonmeasurable selectors of countable group actions
Given a set X, a countable group H acting on it and a σ-finite H-invariant measure m on X, we study conditions which imply that each selector of H-orbits is nonmeasurable with respect to any H-invariant extension of m.
On nonmeasurable subgroups of the real line.
On pointwise ergodic theorems for positive operators
On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II
On Regularities of the Distribution of Special Sequences.
On Rudolph's representation of aperiodic flows
On separation properties for families of probability measures.
On sets under certain transformations in RN.
On small stochastic perturbations of mappings of the unit interval
On solvability of the cohomology equation in function spaces
Let T be an endomorphism of a probability measure space (Ω,𝓐,μ), and f be a real-valued measurable function on Ω. We consider the cohomology equation f = h ∘ T - h. Conditions for the existence of real-valued measurable solutions h in some function spaces are deduced. The results obtained generalize and improve a recent result of Alonso, Hong and Obaya.