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Completely nonmeasurable unions

Robert Rałowski, Szymon Żeberski (2010)

Open Mathematics

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 ⊆ $𝕀$ of X contains uncountably many pairwise disjoint subfamilies , with $𝕀$ -Bernstein unions ∪ (a subset A ⊆ X is $𝕀$ -Bernstein if A and X A meet each Borel $𝕀$ -positive subset...

Completeness of the set of sub- $σ$ -algebras.

Wang, Xikui (1993)

International Journal of Mathematics and Mathematical Sciences

Complexité des boréliens à coupes dénombrables

Dominique Lecomte (2000)

Fundamenta Mathematicae

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 $σ$ -algebra in compact Hausdorff spaces

Charles Stegall (1993)

Acta Universitatis Carolinae. Mathematica et Physica

Construction of an Uncountable Difference between Φ(B) and $Φ_{f} (B)$

Josh Campbell, David Swanson (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

We construct a set B and homeomorphism f where f and $f^{- 1}$ 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

Jack Brown (1992)

Fundamenta Mathematicae

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 $F_{σ}$ -supported ideals

Jacek Hejduk (1997)

Colloquium Mathematicae

Coordinatewise decomposition of group-valued Borel functions

Benjamin D. Miller (2007)

Fundamenta Mathematicae

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.

Displaying 21 – 31 of 31

Completely nonmeasurable unions

Completeness of the set of sub- $σ$ -algebras.

Complexité des boréliens à coupes dénombrables

Concerning a certain $σ$ -algebra in compact Hausdorff spaces

Construction of an Uncountable Difference between Φ(B) and $Φ_{f} (B)$

Continuous-, derivative-, and differentiable-restrictions of measurable functions

Convergence with respect to $F_{σ}$ -supported ideals

Coordinatewise decomposition of group-valued Borel functions

Corrections : «Les dérivations analytiques»

Correspondence Between Semi-Measures and Small Systems

Covering theorems for uniqueness and extended uniqueness sets

Currently displaying 21 – 31 of 31