On extension of submeasures
On finitely subadditive outer measures and modularity properties.
On functional polynomials spanned by characters of unitary representations. (Summary).
On lattice-topological properties of general Wallman spaces.
On maximal measures with respect to a lattice.
On Measurability of Uncountable Unions of Measurable Sets
On normal lattices and Wallman spaces.
On outer measures and semi-separation of lattices.
On some extensions of -finite measures.
On some properties of Hausdorff content related to instability.
On some properties of sets with positive measure
On submeasures. II.
On the average of inner and outer measures
On the Basic Extension Theorem in Measure Theory.
On the complexity of sums of Dirichlet measures
Let be the set of all Dirichlet measures on the unit circle. We prove that is a non Borel analytic set for the weak* topology and that is not norm-closed. More precisely, we prove that there is no weak* Borel set which separates from (or even , the set of all measures singular with respect to every measure in . This extends results of Kaufman, Kechris and Lyons about and and gives many examples of non Borel analytic sets.
On the duality between -modulus and probability measures
Motivated by recent developments on calculus in metric measure spaces , we prove a general duality principle between Fuglede’s notion [15] of -modulus for families of finite Borel measures in and probability measures with barycenter in , with dual exponent of . We apply this general duality principle to study null sets for families of parametric and non-parametric curves in . In the final part of the paper we provide a new proof, independent of optimal transportation, of the equivalence...
On the extension of measures.
We give necessary and sufficient conditions for a totally ordered by extension family (Ω, Σx, μx)x ∈ X of spaces of probability to have a measure μ which is an extension of all the measures μx. As an application we study when a probability measure on Ω has an extension defined on all the subsets of Ω.
On the extremality of regular extensions of contents and measures
Let be an algebra and a lattice of subsets of a set . We show that every content on that can be approximated by in the sense of Marczewski has an extremal extension to a -regular content on the algebra generated by and . Under an additional assumption, we can also prove the existence of extremal regular measure extensions.
On the inner Daniell-Stone and Riesz representation theorems.
On the instability of Hausdorff content.