On Alexandrov lattices.
On asymptotic density and uniformly distributed sequences
Assuming Martin's axiom we show that if X is a dyadic space of weight at most continuum then every Radon measure on X admits a uniformly distributed sequence. This answers a problem posed by Mercourakis [10]. Our proof is based on an auxiliary result concerning finitely additive measures on ω and asymptotic density.
On barycentrs in non-compact sets
On certain Wallman spaces.
On compact spaces carrying Radon measures of uncountable Maharam type
If Martin’s Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable space, then there is a continuous surjection from X onto .
On compact spaces carrying random measures of large Maharam type
On compactness of lattices.
On constructing finite, finitely subadditive outer measures, and submodularity.
On extension of Baire submeasures
On finitely subadditive outer measures and modularity properties.
On generators of shy sets on Polish topological vector spaces.
On lattice-topological properties of general Wallman spaces.
On maximal measures with respect to a lattice.
On measure zero sets in topological vector spaces.
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 normal and strongly normal lattices.
On normal lattices and separation and semi-separation of lattices.
On outer measures and semi-separation of lattices.
On Pettis integral and Radon measures
Assuming the continuum hypothesis, we construct a universally weakly measurable function from [0,1] into a dual of some weakly compactly generated Banach space, which is not Pettis integrable. This (partially) solves a problem posed by Riddle, Saab and Uhl [13]. We prove two results related to Pettis integration in dual Banach spaces. We also contribute to the problem whether it is consistent that every bounded function which is weakly measurable with respect to some Radon measure is Pettis integrable....
On Prohorov spaces