相关论文: Discrepancy and approximation of absolutely contin…
We study here the error of numerical integration on metric measure spaces adapted to a decomposition of the space into disjoint subsets. We consider both the error for a single given function, and the worst case error for all functions in a…
We consider a discrete-time, continuous-state random walk with steps uniformly distributed in a disk of radius of $h$. For a simply connected domain $D$ in the plane, let $\omega_h(0,\cdot;D)$ be the discrete harmonic measure at $0\in D$…
A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.
We characterize the gauge profile of $\mathcal{D}_s$, the set of reals with effective dimension $s$, and $\mathcal{D}_{\leq s}$, the set of reals with effective dimension $\leq s$. Let $W(s)$ be the set of reals that are $s$-well…
We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…
Following our previous work on copula-based nonsymmetric dependence measures, we introduce similar measures for discrete random variables. The measures cover the range between two extremes: independence and complete dependence, which take…
In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.
We show that for uniform domains $\Omega\subseteq \mathbb{R}^{d+1}$ whose boundaries satisfy a certain nondegeneracy condition that harmonic measure cannot be mutually absolutely continuous with respect to $\alpha$-dimensional Hausdorff…
The distortion of six different intrinsic metrics and quasi-metrics under conformal and quasiregular mappings is studied in a few simple domains $G\subsetneq\mathbb{R}^n$. The already known inequalities between the hyperbolic metric and…
We propose a protocol to test whether the postulate of a measurement acting as an instantaneous projection onto an eigenstate of the measurement apparatus is compatible with physical reality. This approach is solely based on repeated…
The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…
We address several different Casimir experiments where theory and experiment disagree. First out is the classical Casimir force measurement between two metal half spaces; here both in the form of the torsion pendulum experiment by Lamoreaux…
As a generalization of Dempster-Shafer theory, the theory of D numbers is a new theoretical framework for uncertainty reasoning. Measuring the uncertainty of knowledge or information represented by D numbers is an unsolved issue in that…
Measuring the effect of gravity on antimatter is a longstanding problem in physics that has significant implications for our understanding of the fundamental nature of the universe. Here, we present a technique to measure the gravitational…
There are two definitions of the measurable functional on the topological vector space: as a linear and measurable real-valued function and as a pointwise limit of the sequence of the continious linear functionals. In general case they are…
In this paper we address questions of continuity and atomicity of conformal ending measures for arbitrary non-elementary Kleinian groups. We give sufficient conditions under which such ending measures are purely atomic. Moreover, we will…
In the approximate integration some inequalities between the quadratures and the integrals approximated by them are called \emph{extremalities}. On the other hand, the set of all quadratures is convex. We are trying to find possible…
The spherical cap discrepancy is a prominent measure of uniformity for sets on the d-dimensional sphere. It is particularly important for estimating the integration error for certain classes of functions on the sphere. Building on a…
Consider a measurable space with an atomless finite vector measure. This measure defines a mapping of the $\sigma$-field into an Euclidean space. According to the Lyapunov convexity theorem, the range of this mapping is a convex compactum.…
Divergence functions are interesting discrepancy measures. Even though they are not true distances, we can use them to measure how separated two points are. Curiously enough, when they are applied to random variables, they lead to a notion…