Related papers: Existence of doubling measures via generalised nes…
We study measures on the configuration spaces of two type particles. Gibbs measures on the such spaces are described. Main properties of corresponding relative energies densities and correlation functions are considered. In particular, we…
We give a sufficiently detailed account on the construction of marked Gibbs measures in the high temperature and low fugacity regime. This is proved for a wide class of underlying spaces and potentials such that stability and integrability…
General Markov chains with a countably additive transition probability in arbitrary phase space are considered. Markov operators extend from the space of countably additive measures to the space of finitely additive measures. In the…
We investigate properties which remain invariant under the action of quasi-M\"obius maps of quasi-metric spaces. A metric space is called doubling with constant D if every ball of finite radius can be covered by at most D balls of half the…
We study locally compact, locally geodesically complete, locally CAT(k) spaces (GCBA(k)-spaces). We prove a Croke-type local volume estimate only depending on the dimension of these spaces. We show that a local doubling condition, with…
In a separably connected space any two points are contained in a separable connected subset. We show a mechanism that takes a connected bounded metric space and produces a complete connected metric space whose separablewise components form…
Recently, Yang, Yuan and Zhang [Doubling properties of self-similar measures and Bernoulli measures on self-affine Sierpinski sponges, Indiana Univ. Math. J., 73 (2024), 475-492] characterized when a self-similar measure satisfying the open…
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We overview the theory of classical MDS, along with its…
We consider a topological space with its subbase which induces a coding for each point. Every second-countable Hausdorff space has a subbase that is the union of countably many pairs of disjoint open subsets. A dyadic subbase is such a…
The property of measure concentration is that an arbitrary 1-Lipschitz function $f:X\to \mathbb{R}$ on an mm-space $X$ is almost close to a constant function. In this paper, we prove that if such a concentration phenomenon arise, then any…
Incompatible, i.e. non-jointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a…
Many results in mass partitions are proved by lifting $\mathbb{R}^d$ to a higher-dimensional space and dividing the higher-dimensional space into pieces. We extend such methods to use lifting arguments to polyhedral surfaces. Among other…
The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the…
We show that the existence of disintegration for cylindrical measures follows from a general disintegration theorem for countably additive measures.
In a mass partition problem, we are interested in finding equitable partitions of smooth measures in $\mathbb{R}^d$. In this manuscript, we study the problem of finding simultaneous bisections of measures using scaled copies of a prescribed…
We construct a multiset space $\mathbb{N}[X]$ over a metric space $X$ that simultaneously enjoys desirable topological properties and admits a natural matching metric $d_{\mathbb{N}[X]}$, making it a metrizable abelian topological monoid…
In this paper, generalized metrics mean metrics taking values in general linearly ordered Abelian groups. Using the Hahn fields, we first prove that for every generalized metric space, if the set of the Archimedean equivalence classes of…
We explore the relationship in metric spaces between different properties related to the Besicovitch covering theorem, and also consider weak versions of doubling, in connection to the non-uniqueness of centers and radii in arbitrary metric…
We characterize uniformly perfect, complete, doubling metric spaces which embed bi- Lipschitzly into Euclidean space. Our result applies in particular to spaces of Grushin type equipped with Carnot-Carath\'eodory distance. Hence we obtain…