Some remarks on Suslin sections
Some remarks on the metrical transitivity of invariant and quasi-invariant measures
Some Results on Analytic Spaces and Semi-Analytic Functions with Regard to Gambling Theory.
Some results on projection of planar sets
In this paper we define certain types of projections of planar sets and study some properties of such projections.
Some results on sets of positive measure in a metric space
Some topological properties of -covering sets
We prove the following theorems: There exists an -covering with the property . Under there exists such that is not an -covering or is not an -covering]. Also we characterize the property of being an -covering.
Some uniformization results
Some Vitali theorems for Lebesgue Measure.
Spaces with Measurable Diagonal
Split Faces and Projective Sets in a Metrizable Compact Convex Set.
Stretched shadings and a Banach measure that is not scale-invariant
It is shown that if A ⊂ ℝ has the same constant shade with respect to all Banach measures, then the same is true of any similarity transformation of A and the shade is not changed by the transformation. On the other hand, if A ⊂ ℝ has constant μ-shade with respect to some fixed Banach measure μ, then the same need not be true of a similarity transformation of A with respect to μ. But even if it is, the μ-shade might be changed by the transformation. To prove such a μ exists, a Hamel basis with some...
Strong Fubini properties for measure and category
Let (FP) abbreviate the statement that holds for every bounded function f: [0,1]² → ℝ whenever each of the integrals involved exists. We shall denote by (SFP) the statement that the equality above holds for every bounded function f: [0,1]² → ℝ having measurable vertical and horizontal sections. It follows from well-known results that both of (FP) and (SFP) are independent of the axioms of ZFC. We investigate the logical connections of these statements with several other strong Fubini type properties...
Strong Fubini properties of ideals
Let I and J be σ-ideals on Polish spaces X and Y, respectively. We say that the pair ⟨I,J⟩ has the Strong Fubini Property (SFP) if for every set D ⊆ X× Y with measurable sections, if all its sections are in J, then the sections are in I for every y outside a set from J (“measurable" means being a member of the σ-algebra of Borel sets modulo sets from the respective σ-ideal). We study the question of which pairs of σ-ideals have the Strong Fubini Property. Since CH excludes this phenomenon completely,...
Sur la mesurabilité d'une fonction numérique par rapport à une famille d'ensembles
Sur la séparabilité et la continuité des fonctions aléatoires
Sur le lemme de mesurabilité de Doob
Sur les convexes compacts dont l’ensemble des points extrémaux est -analytique
Sur les fonctions vectorielles approximativement continues
Symmetric porosity of symmetric Cantor sets
The Baire and Borel measure