Related papers: Convergence from below suffices
Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy and is…
Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the…
If $A$ and $B$ are two bounded sets of reals, Ruzsa proved a precise lower bound of the measure of the sumset $A+B$ involving the ratio $\lambda(A)/\lambda(B)$. De Roton established a structural result about the critical sets of this lower…
We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid version allows us to formulate a strong form of extensionality,…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.
The aim of this paper is to to show the admissibility of some class of Frechet spaces (see Definition 2.3). In particular, this generalizes the main results of [3]. As an application, we show the admissibility of a large class modular…
The purpose of this paper is to show that the Rudin-Carleson interpolation theorem is a direct corollary of Fatou's much older interpolation theorem (of 1906).
We provide a compactness principle which is applicable to different formulations of Plateau's problem in codimension one and which is exclusively based on the theory of Radon measures and elementary comparison arguments. Exploiting some…
It is shown that the approximating functions used to define the Bochner integral can be formed using geometrically nice sets, such as balls, from a differentiation basis. Moreover, every appropriate sum of this form will be within a…
A known Hardy-Littlewood theorem asserts that if both the function and its conjugate are of bounded variation, then their Fourier series are absolutely convergent. It is proved in the paper that the same result holds true for functions on…
We propose a new approach at Fermat's Last Theorem (FLT) solution: for each FLT equation we associate a polynomial of the same degree. The study of the roots of the polynomial allows us to investigate the FLT validity. This technique,…
The aim of this article is to establish new two-functions minimax inequalities extending classical results such as Simons' minimax theorem. Our results will be proved in a non-compact setting. We also prove, under general conditions, that…
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.
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.
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
We give a new proof of Fatou's theorem: {\em if an algebraic function has a power series expansion with bounded integer coefficients, then it must be a rational function.} This result is applied to show that for any non--trivial completely…
We show that if a numerical method is posed as a sequence of operators acting on data and depending on a parameter, typically a measure of the size of discretization, then consistency, convergence and stability can be related by a…
A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.
The Lowest Landau Level (LLL), long distance theory of Composite Fermions (CF) developed by Murthy and myself is minimally extended to all distances, guided by very general principles. The resulting theory is mathematically consistent, and…