Related papers: Correction of metrics

A review of the state of the art of the comparison between any two different modes of convergence of sequences of measurable functions is carried out with focus on the algebraic structure of the families under analysis. As a complement of…

Hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them. Our main result describes the behavior of the triangular ratio metric under…

We classify the complete metrics of nonnegative sectional curvature on M^2xR^2, where M^2 is any compact 2-manifold.

In this paper we present full characterizations of multifunctions admitting a measurable by seminorm selector in Frechet spaces.

We prove that the Bergman and the Teichmuller metrics are equivalent on Teichmuller spaces.

We introduce a notion being a $k$-fold Lebesgue function for measure preserving transformations, where any $2$-fold Lebesgue function is just ordinary Lebesgue. We discuss how this new metrical isomorphisms invariant of dynamical systems is…

In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.

Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…

We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of…

We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators…

For essentially bounded functions on a (closed) compact Riemannian manifold, the noncommutative residue and the Dixmier trace formulation of the noncommutative integral are shown to equate to a multiple of the Lebesgue integral. The…

The question how to certify non-negativity of a polynomial function lies at the heart of Real Algebra and also has important applications to Optimization. In this article we investigate the question of non-negativity in the context of…

Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…

Metrics on Grassmannians have a wide array of applications: machine learning, wireless communication, computer vision, etc. But the available distances between subspaces of distinct dimensions present problems, and the dimensional asymmetry…

Diversities are a generalization of metric spaces in which a non-negative value is assigned to all finite subsets of a set, rather than just to pairs of points. Here we provide an analogue of the theory of negative type metrics for…

The aim of this paper is to investigate the equivalence conditions for uniform perfectness of quasi-metric spaces. We also obtain the invariant property of uniform perfectness under quasim\"obius maps in quasi-metric spaces. In the end, two…

We prove certain type symmetric inequalities in $\textbf{R}^{2}$ and $\textbf{R}^3$, that ocur in many problems of analysis. These inequalities are generalizations of the Jensen's inequality from one variable to two and three variables

We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM} and developed the idea further in \cite{AS}. In this paper we study locally $M$-metrizable spaces and the products of $M$-metrizable spaces. Finally we…

We introduce a class of functional analogs of the symmetric difference metric on the space of coercive convex functions on $\mathbb{R}^n$ with full-dimensional domain. We show that convergence with respect to these metrics is equivalent to…

We obtain convolution inequalities in Lebesgue and Lorentz spaces with power weights when the functions involved are assumed to be radially symmetric. We also present applications of these results to inequalities for Riesz potentials of…