On natural invariant measures on generalised iterated function systems.
On Nikodym-type sets in high dimensions
We prove that the complement of a higher-dimensional Nikodym set must have full Hausdorff dimension.
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 normal and strongly normal lattices.
On normal lattices and separation and semi-separation of lattices.
On normal lattices and Wallman spaces.
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,...).
On outer measures and semi-separation of lattices.
On pointwise limits of sequences of -continuous functions
On products of admissible liftings and densities.
On projection measurability of functions and multifunctions
On projection of nonseparable Souslin and Borel sets along separable spaces
On projective limits of probability spaces
On qualitative cluster sets
On -dimensional integrals in -space
On random fractals with infinite branching: definition, measurability, dimensions
We investigate the definition and measurability questions of random fractals with infinite branching, and find, under certain conditions, a formula for the upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.