Related papers: Haar measure for non-Hausdorff locally compact gro…

We give a detailed and unified survey of equivariant $KK$-theory over locally compact, second countable, locally Hausdorff groupoids. We indicate precisely how the "classical" proofs relating to the Kasparov product can be used almost…

We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to…

We examine the analogues for the respective categories of locales of two well-known results about regularity and effectiveness of some categories of spaces. We show that the category of compact regular locales is effective regular…

Compact metric spaces form an important class of metric spaces, but the category that they define lacks many important properties such as completeness and cocompleteness. In recent studies of "metric domain theory" and Stone-type dualities,…

Let $G$ and $H$ be locally compact groups with fixed two-side-invariant Haar measures. A polyhomomorphism $G\to H$ is a closed subgroup $R\subset G\times H$ with a fixed Haar measure, whose marginals on $G$ and $H$ are dominated by the Haar…

We show that if K is Rosenthal compact which can be represented by functions with countably many discontinuities then every Radon measure on K is countably determined. We also present an alternative proof of the result stating that every…

Let G be a second countable, locally compact group and let f be a continuous Herz-Schur multiplier on G. Our main result gives the existence of a (not necessarily uniformly bounded) strongly continuous representation on a Hilbert space,…

In this note, we extend the characterization of dyadic Lipschitz regularity of functions to non-atomic probability spaces, using generalized Haar systems.

It is shown that a locally compact groupoid with open range map does not always admit a Haar system. It then is shown how to construct a Haar system if the stability groupoid and the quotient by the stability groupoid both admit one.

This article is concerned with measure equivalence and uniform measure equivalence of locally compact, second countable groups. We show that two unimodular, locally compact, second countable groups are measure equivalent if and only if they…

A homeomorphism on a compact metric space is said hyper-expansive if every pair of different compact sets are separated by the homeomorphism in the Hausdorff metric. We characterize such dynamics as those with a finite number of orbits and…

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case…

We present a generalization of Hirschman's entropic uncertainty principle for locally compact abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups,…

Methods for measuring convexity defects of compacts in R^n abound. However, none of the those measures seems to take into account continuity. Continuity in convexity measure is essential for optimization, stability analysis, global…

Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author…

The paper presents some weak compactness criterion for a subset $M$ of the set $\mathfrak{RM}_b(T,\mathcal{G})$ of all positive bounded Radon measures on a Hausdorff topological space $(T,\mathcal{G})$ similar to the Prokhorov criterion for…

We introduce a novel notion of {\it local spectral gap} for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action $\Gamma\curvearrowright G$, whenever $\Gamma$ is a dense…

We show that Haar measures of connected semisimple groups, embedded via a representation into a matrix space, have a homogeneous asymptotic limit when viewed from far away and appropriately rescaled. This is still true if the Haar measure…

We extend the definition of topological pressure to locally compact Hausdorff spaces, and we demonstrate a "variational principle" comparing the topological and measure theoretic pressures. Given a continuous $\mathbb{Z}_+^N$-action $T$…

We prove a Freiman-type theorem for locally compact abelian groups. If A is a subset of a locally compact abelian group with Haar measure m and m(nA) < n^dm(A) for all n>d log d then we describe A in a way which is tight up to logarithmic…