On a class of arithmetical sets
On a decomposition of Banach spaces
By using D. Preiss' approach to a construction from a paper by J. Matoušek and E. Matoušková, and some results of E. Matoušková, we prove that we can decompose a separable Banach space with modulus of convexity of power type p as a union of a ball small set (in a rather strong symmetric sense) and a set which is Aronszajn null. This improves an earlier unpublished result of E. Matoušková. As a corollary, in each separable Banach space with modulus of convexity of power type p, there exists a closed...
On a measurable set
On a paper by Karel Prikry concerning Ulam's problem on families of measures
On A Paper Of Saha And Ray
On a question of H. Kraljevic.
On a set in under coordinate transformations
On a theorem of Holický and Zelený concerning Borel maps without -compact fibers
The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.
On absolutely measurable sets
On almost invariant subsets of the real line
On an Abstract Formulation of Regularity
On analytic-dense Blackwell sets
On bimeasurable images of universally measurable sets
On Borel, Baire and Lebesgue sets.
On Borel-measurable collections of countable-dimensional sets
On Certain Generalized Probability Domains
On certain regularity properties of Haar-null sets
Let X be an abelian Polish group. For every analytic Haar-null set A ⊆ X let T(A) be the set of test measures of A. We show that T(A) is always dense and co-analytic in P(X). We prove that if A is compact then T(A) is dense, while if A is non-meager then T(A) is meager. We also strengthen a result of Solecki and we show that for every analytic Haar-null set A, there exists a Borel Haar-null set B ⊇ A such that T(A)∖ T(B) is meager. Finally, under Martin’s Axiom and the negation of Continuum Hypothesis,...
On Certain Transformations Of Sets Of Positive Measure
On certaintransformations of sets of positive measure.
On completion of measures on a --ring