Related papers: Tarski Measure
The paper is devoted to one of the important notions of the shape theory: that of strong movability, which was primarily introduced by K. Borsuk for metrizable compacts. A strong movability criterion is proved for topological spaces, which…
We study a compactification of the space of invariant probability measures for a transitive countable Markov shift. We prove that it is affine homeomorphic to the Poulsen simplex. Furthermore, we establish that, depending on a combinatorial…
In this paper we give explicit gauge invariant Lagrangian formulation for massive theories based on mixed symmetry tensors \Phi_{[\mu\nu],\alpha}, T_{[\mu\nu\alpha],\beta} and R_{[\mu\nu],[\alpha\beta]} both in Minkowski as well as in…
We use Pesin theory to study possible equilibrium measures for piecewise monotone maps of the interval. The maps may have unbounded derivative.
Mass-stationarity means that the origin is at a typical location in the mass of a random measure. It is an intrinsic characterisation of Palm versions with respect to stationary random measures. Stationarity is the special case when the…
We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller…
We define and study a probability monad on the category of complete metric spaces and short maps. It assigns to each space the space of Radon probability measures on it with finite first moment, equipped with the Kantorovich-Wasserstein…
We suggest a new method of describing invariant measures on Markov compacta and path spaces of graphs, and thus of describing characters of some groups and traces of AF-algebras. The method relies on properties of filtrations associated…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone $\cal R$ of distance matrices, and consider geometric and probabilistic problems connected with this object. The notion of the universal distance…
We show, following W. Holsztynski, that there exists a continuous metric d on the set of real numbers R such that any finite metric space is isometrically embeddable into (R,d).
For a Dunford-Schwartz operator in a fully symmetric space of measurable functions of an arbitrary measure space, we prove pointwise convergence of the conventional and weighted ergodic averages.
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
The generalization of the Jessen-Marcinkiewicz-Zygmund-type theorem for the abstract space with measure was obtained in current paper. Some applications to classical harmonic analysis were reviewed.
We present a complete study of measure-theoretic area formulas in metric spaces, providing different measurability conditions.
We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…
This article fits in the context of the approach to topological problems in terms of the underlying convergence space structures, and serves as yet another illustration of the power of the method. More specifically, we spell out…
A subspace arrangement is a finite collection of affine subspaces in $\mathbb{R}^n$. One of the main problems associated to arrangements asks up to what extent the topological invariants of the union of these spaces, and of their complement…
The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. We develop…
Extending the `metric spaces' of Lawvere, we study `real metrics', with values in the extended real line. Formally, this ordered set is a symmetric monoidal closed category, and our structures are enriched categories on the latter.…