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Can we assign the Borel hulls in a monotone way?

Márton Elekes, András Máthé (2009)

Fundamenta Mathematicae

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/ $G_{δ}$ 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 $G_{δ}$ hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent....

Category bases.

Detlefsen, M., Szymański, Andrzej (1993)

International Journal of Mathematics and Mathematical Sciences

Certain transformations $T_{ω}$ and Lebesgue measurable sets of positive measure

Mukul Pal, Mrityunjoy Nath (1999)

Czechoslovak Mathematical Journal

Champs mesurables d'espaces sousliniens

Claude Delode (1977)

Annales de l'I.H.P. Probabilités et statistiques

Champs mesurables et multisections

C. Delode, O. Arino, J.-P. Penot (1976)

Annales de l'I.H.P. Probabilités et statistiques

Characterization of σ-porosity via an infinite game

Martin Doležal (2012)

Fundamenta Mathematicae

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 $K$ -analytic

Michel Talagrand (1985)

Annales de l'institut Fourier

We construct a Choquet simplex $K$ whose set of extreme points $T$ is $𝒦$ -analytic, but is not a $𝒦$ -Borel set. The set $T$ has the surprising property of being a $K_{σ δ}$ set in its Stone-Cech compactification. It is hence an example of a $K_{σ δ}$ set that is not absolute.

Classical hierarchies form a modern standpoint. Part III. BP-sets

John Burgess, Richard Lockhart (1983)

Fundamenta Mathematicae

Classical hierarchies from a modern standpoint. Part I. C-sets

John Burgess (1983)

Fundamenta Mathematicae

Classical hierarchies from a modern standpoint. Part II. R-sets

John Burgess (1983)

Fundamenta Mathematicae

Classification and extension by the transfinite induction

Michal Šabo (1979)

Mathematica Slovaca

Classification of $s i g m a$ -ideals

Marek Balcerzak (1987)

Mathematica Slovaca

Combinatorics on σ-algebras and problem of Banach

Andrzej Pelc (1984)

Fundamenta Mathematicae

Compactness in the sense of the convergence with respect to a small system

Jacek Hejduk, Eliza Wajch (1989)

Mathematica Slovaca

Compacts de fonctions mesurables et filtres non mesurables

Michel Talagrand (1980)

Studia Mathematica

Complementation in the lattice of Borel structures

H. Sarbadhikari, K. P. S. Bhaskara Rao, E. Grzegorek (1974)

Colloquium Mathematicae

Complementation in the lattice of Borel structures

B. Aniszczyk (1987)

Colloquium Mathematicae

Complete pairs of coanalytic sets

Jean Saint Raymond (2007)

Fundamenta Mathematicae

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 $ω^{ω}$ there exists a continuous function $f : ω^{ω} \to X$ such that $f^{- 1} (C ₀) = D ₀$ and $f^{- 1} (C ₁) = D ₁$ . We give several explicit examples of complete pairs of coanalytic sets.

Complete Spaces and Zero-One Measures.

Wolfgang Adamski (1976)

Manuscripta mathematica

Completely additive disjoint system of Baire sets is of bounded class

David Preiss (1974)

Commentationes Mathematicae Universitatis Carolinae

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