On Stone-type extensions for group-valued measures
On Strict Ergodicity.
On strictly ergodic models for commuting ergodic transformations
On strong differentiability of integrals along different directions.
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 liftings for projective limits
We discuss the permanence of strong liftings under the formation of projective limits. The results are based on an appropriate consistency condition of the liftings with the projective system called "self-consistency", which is fulfilled in many situations. In addition, we study the relationship of self-consistency and completion regularity as well as projective limits of lifting topologies.
On strong mixing and weak convergence for groups of operators
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 strongly additive set functions
On strongly measure replete lattices and the general Wallman remainder
On strongly Pettis integrable functions in locally convex spaces.
Some characterizations have been given for the relative compactness of the range of the indefinite Pettis integral of a function on a complete finite measure space with values in a quasicomplete Hausdorff locally convex space. It has been shown that the indefinite Pettis integral has a relatively compact range if the functions is measurable by seminorm. Separation property has been defined for a scalarly measurable function and it has been proved that a function with this property is integrable...
On Subadditive Processes on Direct Product of Countable Amenable Groups
On submeasures. II.
On subrelations of ergodic measured type III equivalence relations
We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.
On subseries.
On subspaces of measurable real functions.
On summability of measures with thin spectra
We study different conditions on the set of roots of the Fourier transform of a measure on the Euclidean space, which yield that the measure is absolutely continuous with respect to the Lebesgue measure. We construct a monotone sequence in the real line with this property. We construct a closed subset of which contains a lot of lines of some fixed direction, with the property that every measure with spectrum contained in this set is absolutely continuous. We also give examples of sets with such property...
On superpositional measurability of semi-Carathéodory multifunctions
It is shown that product weakly measurable lower weak semi-Carathéodory multifunction is superpositionally measurable.
On superpositionally measurable multifunctions