On minimal generators of σ-fields
On mixing transformations.
On modular set functions and measures
On multiplicity functions and Lebesgue area
On multivalued martingales, multimeasures and multivalued Radon-Nikodym property
In this paper we prove a representation result for essentially bounded multivalued martingales with nonempty closed convex and bounded values in a real separable Banach space. Then we turn our attention to the interplay between multimeasures and multivalued Riesz representations. Finally, we give the multivalued Radon-Nikodym property.
On natural invariant measures on generalised iterated function systems.
On nearly radial marginals of high-dimensional probability measures
Suppose that is an absolutely continuous probability measure on n, for large . Then has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if , then there exist -dimensional marginals of that are -far from being sphericallysymmetric, in an appropriate sense. Here is a universal constant.
On Nikodym-type sets in high dimensions
We prove that the complement of a higher-dimensional Nikodym set must have full Hausdorff dimension.
On non-ergodic versions of limit theorems
The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.
On nonmeasurable images
Let be a Polish ideal space and let be any set. We show that under some conditions on a relation it is possible to find a set such that is completely -nonmeasurable, i.e, it is -nonmeasurable in every positive Borel set. We also obtain such a set simultaneously for continuum many relations Our results generalize those from the papers of K. Ciesielski, H. Fejzić, C. Freiling and M. Kysiak.
On nonmeasurable selectors of countable group actions
Given a set X, a countable group H acting on it and a σ-finite H-invariant measure m on X, we study conditions which imply that each selector of H-orbits is nonmeasurable with respect to any H-invariant extension of m.
On nonmeasurable subgroups of the real line.
On nonparadoxical sets
On non-zero dimensional atoms
On normal and strongly normal lattices.
On normal lattices and separation and semi-separation of lattices.
On normal lattices and Wallman spaces.
On Obtaining a Stationary Process Isomorphic to a Given Process with a Desired Distribution.
On one generalization of the weakly compactly generated B-spaces
On Ordinary and Standard Lebesgue Measures on
New concepts of Lebesgue measure on are proposed and some of their realizations in the ZFC theory are given. Also, it is shown that Baker’s both measures [1], [2], Mankiewicz and Preiss-Tišer generators [6] and the measure of [4] are not α-standard Lebesgue measures on for α = (1,1,...).