Borel sets of exact class
Borel sets with σ-compact sections for nonseparable spaces
We prove that every (extended) Borel subset E of X × Y, where X is complete metric and Y is Polish, can be covered by countably many extended Borel sets with compact sections if the sections , x ∈ X, are σ-compact. This is a nonseparable version of a theorem of Saint Raymond. As a by-product, we get a proof of Saint Raymond’s result which does not use transfinite induction.
Borel structures for function spaces
Borel-approachable functions
Borel-dense Blackwell spaces are strongly Blackwell
Bounded analytic sets in Banach spaces
Conditions are given which enable or disable a complex space to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of .
Can we assign the Borel hulls in a monotone way?
A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent....
Category bases.
Certain transformations and Lebesgue measurable sets of positive measure
Champs mesurables d'espaces sousliniens
Champs mesurables et multisections
Characterization of σ-porosity via an infinite game
Let X be an arbitrary metric space and P be a porosity-like relation on X. We describe an infinite game which gives a characterization of σ-P-porous sets in X. This characterization can be applied to ordinary porosity above all but also to many other variants of porosity.
Choquet simplexes whose set of extreme points is -analytic
We construct a Choquet simplex whose set of extreme points is -analytic, but is not a -Borel set. The set has the surprising property of being a set in its Stone-Cech compactification. It is hence an example of a set that is not absolute.
Classical hierarchies form a modern standpoint. Part III. BP-sets
Classical hierarchies from a modern standpoint. Part I. C-sets
Classical hierarchies from a modern standpoint. Part II. R-sets
Classification and extension by the transfinite induction
Classification of -ideals
Combinatorics on σ-algebras and problem of Banach
Compactness in the sense of the convergence with respect to a small system