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.
On some properties of transformations of a logic
On stability properties of positive contractions of L¹-spaces associated with finite von Neumann algebras
We extend the notion of Dobrushin coefficient of ergodicity to positive contractions defined on the L¹-space associated with a finite von Neumann algebra, and in terms of this coefficient we prove stability results for L¹-contractions.
On Strict Ergodicity.
On strictly ergodic models for commuting ergodic transformations
On strong laws for generalized L-statistics with dependent data
It is pointed out that a strong law of large numbers for L-statistics established by van Zwet (1980) for i.i.d. sequences, remains valid for stationary ergodic data. When the underlying process is weakly Bernoulli, the result extends even to generalized L-statistics considered in Helmers et al. (1988).
On strong uniform distribution
On strong uniform distribution, II. The infinite-dimensional case
We construct infinite-dimensional chains that are L¹ good for almost sure convergence, which settles a question raised in this journal [N]. We give some conditions for a coprime generated chain to be bad for L² or , using the entropy method. It follows that such a chain with positive lower density is bad for . There also exist such bad chains with zero density.
On Subadditive Processes on Direct Product of Countable Amenable Groups
On the Boundedness of Weyl Sums.
On the coding theorem for decomposable discrete information channels. I
On the coding theorem for decomposable discrete information channels. II
On the Connectedness of Ergodic Systems.
On the countable generator theorem
Let T be a finite entropy, aperiodic automorphism of a nonatomic probability space. We give an elementary proof of the existence of a finite entropy, countable generating partition for T.