On Borel-measurable collections of countable-dimensional sets
On Certain Generalized Probability Domains
On certain regularity properties of Haar-null sets
Let X be an abelian Polish group. For every analytic Haar-null set A ⊆ X let T(A) be the set of test measures of A. We show that T(A) is always dense and co-analytic in P(X). We prove that if A is compact then T(A) is dense, while if A is non-meager then T(A) is meager. We also strengthen a result of Solecki and we show that for every analytic Haar-null set A, there exists a Borel Haar-null set B ⊇ A such that T(A)∖ T(B) is meager. Finally, under Martin’s Axiom and the negation of Continuum Hypothesis,...
On Certain Transformations Of Sets Of Positive Measure
On certain Wallman spaces.
On certaintransformations of sets of positive measure.
On Characterization of Absolutely Continuous Measures on Locally Compact Spaces.
On common extensions of two quasi-measures
On common extensions of two quasi-measures
On compact embedding theorems in weighted Sobolev spaces
On Compactness and Convergence in Spaces of Measures.
On compactness and extreme points of some sets of quasi-measures and measures. II.
On Compactness and Extreme Points of Some Sets of Quasi-Measures and Measures.
On compactness of lattices.
On complete measurability of multifunctions defined on product spaces.
On complete-cocomplete subspaces of an inner product space
In this note we give a measure-theoretic criterion for the completeness of an inner product space. We show that an inner product space is complete if and only if there exists a -additive state on , the orthomodular poset of complete-cocomplete subspaces of . We then consider the problem of whether every state on , the class of splitting subspaces of , can be extended to a Hilbertian state on ; we show that for the dense hyperplane (of a separable Hilbert space) constructed by P. Pták and...
On completion of measures on a --ring
On complex Radon measures. I
On concentration of self-bounding functions.
On Conditions for Unrectifiability of a Metric Space
We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups.