Related papers: An anisotropic inhomogeneous ubiquity Theorem
Here using some methods of combinatorial set theory, particularly the ones related to the construction of independent families of sets and some modified version of the notion of small sets originally introduced by Riecan, Riecan and…
The theory of measurement is employed to elucidate the physical basis of general relativity. For measurements involving phenomena with intrinsic length or time scales, such scales must in general be negligible compared to the (translational…
The concept of measurement is discussed. It is argued that counting process in mathematics is also measurement which requires a basic unit. The idea of scale is put forward. The basic unit itself, which are composed of the infinitesimal of…
The concentration of measure prenomenon roughly states that, if a set $A$ in a product $\Omega^N$ of probability spaces has measure at least one half, ``most'' of the points of $\Omega^N$ are ``close'' to $A$. We proceed to a systematic…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
The almost sure convergence of ergodic averages in Birkhoff's pointwise ergodic theorem is known to fail in the finitely additive setting. We introduce a natural reformulation of almost sure convergence suitable for finitely additive…
We generalize the box and observable distances to those between metric measure spaces with group actions, and prove some fundamental properties. As an application, we obtain an example of a sequence of lens spaces with unbounded dimension…
We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the volume element defined by each…
The transverse group associated to some continuous quantum measuring processes is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an exmaple, the case of a particle whose coordinates are being…
We study generalizations of Reifenberg's Theorem for measures in $\mathbb R^n$ under assumptions on the Jones' $\beta$-numbers, which appropriately measure how close the support is to being contained in a subspace. Our main results, which…
We give new examples and describe the complete lists of all measures on the set of countable homogeneous universal graphs and $K_s$-free homogeneous universal graphs (for $s\geq 3$) that are invariant with respect to the group of all…
Motivated by the random covering problem and the study of Dirichlet uniform approximable numbers, we investigate the uniform random covering problem. Precisely, consider an i.i.d. sequence $\omega=(\omega_n)_{n\geq 1}$ uniformly distributed…
In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group $\Iso(\U)$ of isometries of…
We present a simple solution to a question posed by Candes, Romberg and Tao on the uniform uncertainty principle for Bernoulli random matrices. More precisely, we show that a rectangular k*n random subgaussian matrix (with k < n) has the…
We use moving frame techniques to derive a notion of curvature for a class of piecewise-smooth Riemannian metrics called Regge metrics, showing that it is a measure that simultaneously satisfies the (weak) Cartan structure equations and the…
We present a comprehensive framework for the study of the size and large intersection properties of sets of limsup type that arise naturally in Diophantine approximation and multifractal analysis. This setting encompasses the classical…
Several different versions of the theory of numerosities have been introduced in the literature. Here, we unify these approaches in a consistent frame through the notion of set of labels, relating numerosities with the Kiesler field of…
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…
The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which…