Weakly compactly generated Frechet spaces.
Weakly mixing but not mixing quasi-Markovian processes
Let (f,α) be the process given by an endomorphism f and by a finite partition of a Lebesgue space. Let E(f,α) be the class of densities of absolutely continuous invariant measures for skew products with the base (f,α). We say that (f,α) is quasi-Markovian if . We show that there exists a quasi-Markovian process which is weakly mixing but not mixing. As a by-product we deduce that the set of all coboundaries which are measurable with respect to the ’chequer-wise’ partition for σ × S, where σ is...
Weakly mixing rank-one transformations conjugate to their squares
Utilizing the cut-and-stack techniques we construct explicitly a weakly mixing rigid rank-one transformation T which is conjugate to T². Moreover, it is proved that for each odd q, there is such a T commuting with a transformation of order q. For any n, we show the existence of a weakly mixing T conjugate to T² and whose rank is finite and greater than n.
Weakly mixing transformations and the Carathéodory definition of measurable sets
Let 𝕋 denote the set of complex numbers of modulus 1. Let v ∈ 𝕋, v not a root of unity, and let T: 𝕋 → 𝕋 be the transformation on 𝕋 given by T(z) = vz. It is known that the problem of calculating the outer measure of a T-invariant set leads to a condition which formally has a close resemblance to Carathéodory's definition of a measurable set. In ergodic theory terms, T is not weakly mixing. Now there is an example, due to Kakutani, of a transformation ψ̃ which is weakly mixing but not strongly...
Weakly tight functions and their decomposition.
Weakly α-favourable measure spaces
I discuss the properties of α-favourable and weakly α-favourable measure spaces, with remarks on their relations with other classes.
Weak-star continuous homomorphisms and a decomposition of orthogonal measures
We consider the set of complex-valued homomorphisms of a uniform algebra which are weak-star continuous with respect to a fixed measure . The -parts of are defined, and a decomposition theorem for measures in is obtained, in which constituent summands are mutually absolutely continuous with respect to representing measures. The set is studied for -invariant algebras on compact subsets of the complex plane and also for the infinite polydisc algebra.
Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities
Weighted ergodic theorems along subsequences of density zero.
Weighted ergodic theorems for weakly mixing transformation groups.
In this paper we characterize weakly mixing transformation groups in terms of weighted ergodic theorems.
Weighted integral inequalities for the ergodic maximal operator and other sublinear operators. Convergence of the averages and the ergodic Hilbert transform
Weighted integral inequalities for the nontangential maximal function, Lusin area integral, and Walsh-Paley series
Weighted Lp spaces and pointwise ergodic theorems.
In this paper we give an operator theoretic version of a recent result of F. J. Martín-Reyes and A. de la Torre concerning the problem of finding necessary and sufficient conditions for a nonsingular point transformation to satisfy the Pointwise Ergodic Theorem in Lp. We consider a positive conservative contraction T on L1 of a σ-finite measure space (X, F, μ), a fixed function e in L1 with e > 0 on X, and two positive measurable functions V and W on X. We then characterize the pairs (V,W)...
Weighted multiplicative integral inequalities.
Weighted norm inequalities relating the and the area functions
Weighted weak type inequalities for the ergodic maximal function and the pointwise ergodic theorem
Weights for ergodic square functions
Well-posedness and fractals via fixed point theory.
What’s the price of a nonmeasurable set?
In this note, we prove that the countable compactness of together with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of . This is done by providing a family of nonmeasurable subsets of whose intersection with every non-negligible Lebesgue measurable set is still not Lebesgue measurable. We develop this note in three sections: the first presents the main result, the second recalls known results concerning non-Lebesgue measurability and its relations with the Axiom...
When ℵ₁ many sets are contained in a countably generated σ-field
We discuss the problem when ℵ₁ sets are contained in a σ-generated σ-field on some set X. This is related to a problem raised by K. P. S. Bhaskara Rao and Rae Michael Shortt [Dissertationes Math. 372 (1998)] which we answer. We also briefly discuss generating the family of all subsets from rectangles.