Selected results on measurable selections
Selivanovski hard sets are hard
Let . For n ≥ 2, we prove that if Selivanovski measurable functions from to Z give as preimages of H all Σₙ¹ subsets of , then so do continuous injections.
Separating equivalence classes
Given a countable Borel equivalence relation, I introduce an invariant measuring how difficult it is to find Borel sets separating its equivalence classes. I evaluate these invariants in several standard generic extensions.
Sets with no uncountable Blackwell subsets
Sigma-idéaux polaires et ensembles d'unicité dans les groupes abéliens localement compacts
On étend au cadre des groupes abéliens localement compacts certains résultats obtenus notamment par G. Debs, R. Kaufman, A. Kechris, A. Louveau et J. Saint Raymond sur la structure des fermés d’unicité et d’unicité au sens large du cercle unité. On montre également que de très nombreuses familles de compacts issues de l’Analyse Harmonique sont exactement de troisième classe dans la hiérarchie de Baire. Comme application, on donne une démonstration simple de l’existence d’ensembles de Dirichlet qui...
Solution of a problem of Ulam on countable sequences of sets
Some additive properties of sets of real numbers
Some additive properties of special sets of reals
Some comments on infinite Boolean functions
We introduce infinite Boolean functions and investigate some of their properties.
Some connections between measure, indiscernibility and representation of cuts
Some examples in the theory of Borel sets
Some examples of true sets
Let K(X) be the hyperspace of a compact metric space endowed with the Hausdorff metric. We give a general theorem showing that certain subsets of K(X) are true sets.
Some relations between k-analytic sets and generalized Borel sets
Some remarks about Mycielski ideals
Some Remarks on Indicatrices of Measurable Functions
We show that for a wide class of σ-algebras 𝓐, indicatrices of 𝓐-measurable functions admit the same characterization as indicatrices of Lebesgue-measurable functions. In particular, this applies to functions measurable in the sense of Marczewski.
Some remarks on subgroups of real numbers
Some strongly bounded classes of Banach spaces
We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable reflexive Banach space containing isomorphic copies of every separable uniformly convex Banach 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
Stable families of analytic sets
We give a different proof of the well-known fact that any uncountable family of analytic subsets of a Polish space with the point-finite intersection property must contain a subfamily whose union is not analytic. Our approach is based on the Kunen-Martin theorem.