Complementation in the lattice of Borel structures
Complete duals of C*(X).
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 positivity of entropy and non-Bernoullicity for transformation groups
The existence of non-Bernoullian actions with completely positive entropy is proved for a class of countable amenable groups which includes, in particular, a class of Abelian groups and groups with non-trivial finite subgroups. For this purpose, we apply a reverse version of the Rudolph-Weiss theorem.
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 spaces over finitely additive probabilities
Completeness of the set of sub--algebras.
Completeness of the space of separable measures in the Kantorovich-Rubinshtein metric.
Completion regularity and -additivity of measures on product spaces
Complex continued fractions with restricted entries.
Complex dimensions of self-similar fractal strings and Diophantine approximation.
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.
Compositions of operators with vector valued maps
Concavity of the Lagrangian for quasi-periodic orbits.
Concentrated monotone measures with non-unique tangential behavior in
We show that for every there is a set such that is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and has the -dimensional density between and everywhere in the support.
Concentration of measure and isoperimetric inequalities in product spaces
Concerning a certain -algebra in compact Hausdorff spaces
Concerning Sets of the First Baire Category with Respect to Different Metrics
We prove that if and δ are the Hausdorff metric and the radial metric on the space ⁿ of star bodies in ℝ, with 0 in the kernel and with radial function positive and continuous, then a family ⊂ ⁿ that is meager with respect to need not be meager with respect to δ. Further, we show that both the family of fractal star bodies and its complement are dense in ⁿ with respect to δ.