Related papers: Generalized multi-scale Young measures
In this paper we give an improved upper bound, as compared to the one given in [3] for the number of extreme points of the convex set of all G-invariant probability measures on X*Y with given marginals of full support.
We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also study some properties on the difference between…
In this paper, we present the characterizations of total boundedness, relative compactness and compactness in fuzzy set spaces equipped with the endograph metric. The conclusions in this paper significantly improve the corresponding…
We establish sharp exponential deviation estimates of the information content as well as a sharp bound on the varentropy for the class of convex measures on Euclidean spaces. This generalizes a similar development for log-concave measures…
In this work we consider translation-bounded measures over a locally compact Abelian group $\mathbb{G}$, with particular interest for their so-called diffraction. Given such a measure $\Lambda$, its diffraction $\widehat{\gamma}$ is another…
Let M_n stand for the Plancherel measure on Y_n, the set of Young diagrams with n boxes. A recent result of Stanley (arXiv:0807.0383) says that for certain functions G defined on the set Y of all Young diagrams, the average of G with…
This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a…
We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…
We show the existence of Lebesgue-equivalent conservative and ergodic $\sigma$-finite invariant measures for a wide class of one-dimensional random maps consisting of piecewise convex maps. We also estimate the size of invariant measures…
Gauges, or convex distance functions are, roughly speaking, norms without symmetry. In this paper we intend to quantify how asymmetric a planar gauge can be. We introduce asymmetry measures for smooth gauges and for strictly convex gauges,…
A modified Mimetic gravity (MMG) is proposed as a generalization of general relativity. The model contain a physical metric which is function of an auxiliary (unphysical) metric and a Lyra's metric. We construct different kinds of…
We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space $S=\Gamma\backslash G/K$ is compact. More precisely, given a sequence of homogeneous probability…
We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of…
Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular, we examine the relations between the measure of concordance of an $n$-copula and the…
In this paper, we study the stochastic homogenization for a family of integral functionals with convex and nonstandard growth integrands defined on Orlicz-Sobolev's spaces. One fundamental in this topic is to extend the classical…
Uniform measures are the functionals on the space of bounded uniformly continuous functions that are continuous on every bounded uniformly equicontinuous set. This paper describes the role of uniform measures in the study of convolution on…
This paper shows that finitely additive measures occur naturally in very general Divergence Theorems. The main results are two such theorems. The first proves the existence of pure normal measures for sets of finite perime- ter, which yield…
We study unimodular measures on the space $\mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups…
We construct N-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ generalizing thereby the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge…
The modulus metric (also called the capacity metric) on a domain $D\subset \mathbb{R}^n$ can be defined as $\mu_D(x,y)=\inf\{{\mbox{cap}}\,(D,\gamma)\}$, where ${\mbox{cap}}\,(D,\gamma)$ stands for the capacity of the condenser $(D,\gamma)$…