Compacts de fonctions mesurables et filtres non mesurables
Complementation in the lattice of Borel structures
Complementation in the lattice of Borel structures
Complete pairs of coanalytic sets
Let X be a Polish space, and let C₀ and C₁ be disjoint coanalytic subsets of X. The pair (C₀,C₁) is said to be complete if for every pair (D₀,D₁) of disjoint coanalytic subsets of there exists a continuous function such that and . We give several explicit examples of complete pairs of coanalytic sets.
Complete Spaces and Zero-One Measures.
Completely additive disjoint system of Baire sets is of bounded class
Completely nonmeasurable unions
Assume that no cardinal κ < 2ω is quasi-measurable (κ is quasi-measurable if there exists a κ-additive ideal of subsets of κ such that the Boolean algebra P(κ)/ satisfies c.c.c.). We show that for a metrizable separable space X and a proper c.c.c. σ-ideal II of subsets of X that has a Borel base, each point-finite cover ⊆ of X contains uncountably many pairwise disjoint subfamilies , with -Bernstein unions ∪ (a subset A ⊆ X is -Bernstein if A and X A meet each Borel -positive subset...
Completeness of the set of sub--algebras.
Complexité des boréliens à coupes dénombrables
Nous donnons, pour chaque niveau de complexité Γ, une caractérisation du type "test d'Hurewicz" des boréliens d'un produit de deux espaces polonais ayant toutes leurs coupes dénombrables ne pouvant pas être rendus Γ par changement des deux topologies polonaises.
Concerning a certain -algebra in compact Hausdorff spaces
Construction of an Uncountable Difference between Φ(B) and
We construct a set B and homeomorphism f where f and have property N such that the symmetric difference between the sets of density points and of f-density points of B is uncountable.
Continuous-, derivative-, and differentiable-restrictions of measurable functions
We review the known facts and establish some new results concerning continuous-restrictions, derivative-restrictions, and differentiable-restrictions of Lebesgue measurable, universally measurable, and Marczewski measurable functions, as well as functions which have the Baire properties in the wide and restricted senses. We also discuss some known examples and present a number of new examples to show that the theorems are sharp.
Convergence with respect to -supported ideals
Coordinatewise decomposition of group-valued Borel functions
Answering a question of Kłopotowski, Nadkarni, Sarbadhikari, and Srivastava, we characterize the Borel sets S ⊆ X × Y with the property that every Borel function f: S → ℂ is of the form f(x,y) = u(x) + v(y), where u: X → ℂ and v: Y → ℂ are Borel.
Corrections : «Les dérivations analytiques»
Correspondence Between Semi-Measures and Small Systems
Covering theorems for uniqueness and extended uniqueness sets
Decomposition in the product of a measure space and a Polish space
Definability of small puncture sets
We characterize the class of definable families of countable sets for which there is a single countable definable set intersecting every element of the family.
Definable hereditary families in the projective hierarchy
We show that if ℱ is a hereditary family of subsets of satisfying certain definable conditions, then the reals are precisely the reals α such that . This generalizes the results for measure and category. Appropriate generalization to the higher levels of the projective hierarchy is obtained under Projective Determinacy. Application of this result to the -encodable reals is also shown.