A method of construction of an invariant measure
A method of construction of an invariant measure on a function space is presented.
A method of solving a cocycle functional equation and applications
A "Minimal", Non-Uniquely Ergodic Interval Exchange Transformation.
A Mixing T for which T - T... Is Bernoulli.
A new class of Ornstein transformations with singular spectrum
A new model of the ergodic transformations
A noncompact Choquet theorem
A nonergodic version of Gordin's CLT for integrable stationary processes
A non-regular Toeplitz flow with preset pure point spectrum
Given an arbitrary countable subgroup of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to . For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.
A note on a generalized cohomology equation
We give a necessary and sufficient condition for the solvability of a generalized cohomology equation, for an ergodic endomorphism of a probability measure space, in the space of measurable complex functions. This generalizes a result obtained in [7].
A note on a local ergodic theorem
A note on cocycles in ergodic theory
A note on conservative measures on semigroups.
A note on Lebesgue spaces
A Note on Periodic Points for Ergodic Toral Automorphisms.
A note on the asymptotics of perturbed expanding maps.
A note on the Sierpiński partition.
A probabilistic ergodic decomposition result
Let be a standard probability space. We say that a sub-σ-algebra of decomposes μ in an ergodic way if any regular conditional probability with respect to andμ satisfies, for μ-almost every x∈X, . In this case the equality , gives us an integral decomposition in “-ergodic” components. For any sub-σ-algebra of , we denote by the smallest sub-σ-algebra of containing and the collection of all setsAin satisfyingμ(A)=0. We say that isμ-complete if . Let be a non-empty family...
A property of doubly stochastic densities
A remark on the existence of the ergodic Hilbert transform