On some properties of Hurewicz, Menger, and Rothberger
On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space
We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function with respect to any norming subset there exists a separately increasing function such that the sets of points of discontinuity...
On some properties of sets with positive measure
On some properties of submeasures on MV-algebras
On some properties of the Cantor set
On some properties of the Cantor set and the construction of a class of sets with Cantor set properties
On some properties of transformations of a logic
On spaces of measurable functions
On s-sets in spaces of homogeneous type
Let (X,d,μ) be a space of homogeneous type. We study the relationship between two types of s-sets: relative to a distance and relative to a measure. We find a condition on a closed subset F of X under which F is an s-set relative to the measure μ if and only if F is an s-set relative to δ. Here δ denotes the quasi-distance defined by Macías and Segovia such that (X,δ,μ) is a normal space. In order to prove this result, we prove a covering type lemma and a type of Hausdorff measure based criterion...
On strong differentiability of integrals along different directions.
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 strongly additive set functions
On strongly measure replete lattices and the general Wallman remainder
On submeasures. II.
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 symmetric derivatives and on properties of Zahorski
On systems of null sets
The collection of all sets of measure zero for a finitely additive, group-valued measure is studied and characterised from a combinatorial viewpoint.
On Talagrand's Admissible Net Approach to Majorizing Measures and Boundedness of Stochastic Processes
We show that the main result of [1] on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process with bounded...