Related papers: A random version of Mazur's lemma
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…
This paper studies a robust version of the classic surplus extraction problem, in which the designer knows only that the beliefs of each type belong to some set, and designs mechanisms that are suitable for all possible beliefs in that set.…
Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally…
The paper provides an extension, to fractional order Sobolev spaces, of the classical result of Murat and Brezis which states that the positive cone of elements in $H^{-1}(\Omega)$ compactly embeds in $W^{-1,q}(\Omega)$, for every $q < 2$…
The determination of solutions of many inverse problems usually requires a set of measurements which leads to solving systems of ill-posed equations. In this paper we propose the Landweber iteration of Kaczmarz type with general uniformly…
In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma…
In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of…
The classical Mazur-Ulam theorem establishes that every surjective isometry between normed real vector spaces is an affine transformation. In various applied mathematical settings, however, one encounters maps that preserve distances not…
This paper investigates the problem of extending measure theory to non-separable structures, from generalized descriptive set theory to a broader class of spaces beyond this framework. While various notions, such as the ideal of measure…
In this paper, a conjecture of Mazur, Rubin and Stein concerning certain averages of modular symbols is proved.
An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in…
We establish a general form of Wiener's lemma for measures on locally compact abelian (LCA) groups by using Fourier analysis and the theory of F{{\o}}lner sequences. Our approach provides a unified framework that that encompasses both the…
We give a brief account and a simpler proof of a contour integral formula for the Gauss hypergeometric function. Such formula is alternative to Barnes's integral formula and generalizes the first Barnes Lemma.
The classical multidimensional version of Fatou's lemma (Schmeidler 1970) originally obtained for unconditional expectations and the standard non-negative cone in a finite-dimensional linear space is extended to conditional expectations and…
We provide a version of the celebrated theorem of Koml\'os in which, rather then random quantities, a sequence of finitely additive measures is considered. We obtain a form of the subsequence principle and some applications.
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which…
Finsler's lemma is a classic mathematical result with applications in control and optimization. When the lemma is applied to parameter-dependent LMIs, as such those that arise from problems of robust stability, the extra variables…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
On a compact manifold with boundary, the map consisting of the scalar curvature in the interior and the mean curvature on the boundary is a local surjection at generic metrics. We prove that this result may be localized to compact…
There is a hierarchy of structure conditions for convex sets. In this paper we study a recently defined [3, 8, 9] condition called locally nonconical convexity (abbreviated LNC). Is is easy to show that every strictly convex set is LNC, as…