Page 1 Next

Displaying 1 – 20 of 102

Showing per page

On an Invariant Borel Measure in Hilbert Space

G. Pantsulaia (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold μ of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space ℓ₂ such that μ and any shift μ ( a ) of μ by a vector a μ are neither equivalent nor orthogonal. This extends a result established in [7].

On asymptotic density and uniformly distributed sequences

Ryszard Frankiewicz, Grzegorz Plebanek (1996)

Studia Mathematica

Assuming Martin's axiom we show that if X is a dyadic space of weight at most continuum then every Radon measure on X admits a uniformly distributed sequence. This answers a problem posed by Mercourakis [10]. Our proof is based on an auxiliary result concerning finitely additive measures on ω and asymptotic density.

On Beurling measure algebras

Ross Stokke (2022)

Commentationes Mathematicae Universitatis Carolinae

We show how the measure theory of regular compacted-Borel measures defined on the δ -ring of compacted-Borel subsets of a weighted locally compact group ( G , ω ) provides a compatible framework for defining the corresponding Beurling measure algebra ( G , ω ) , thus filling a gap in the literature.

On certain regularity properties of Haar-null sets

Pandelis Dodos (2004)

Fundamenta Mathematicae

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 G δ 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,...

Currently displaying 1 – 20 of 102

Page 1 Next