scholarly journals A characterization of the Riesz space of measurable functions

1969 ◽  
Vol 135 ◽  
pp. 193-193 ◽  
Author(s):  
J. J. Masterson
Keyword(s):  
Riesz Space ◽  
Measurable Functions

A new characterization of the Haagerup property by actions on infinite measure spaces

2020 ◽  
pp. 1-20
Author(s):  
THIEBOUT DELABIE ◽  
PAUL JOLISSAINT ◽  
ALEXANDRE ZUMBRUNNEN
Keyword(s):  
Finite Measure ◽  
Invariant Mean ◽  
Locally Compact ◽  
Haagerup Property ◽  
Infinite Measure ◽  
Measurable Functions ◽  
Measure Spaces ◽  
Definition Of

The aim of the article is to provide a characterization of the Haagerup property for locally compact, second countable groups in terms of actions on $\unicode[STIX]{x1D70E}$ -finite measure spaces. It is inspired by the very first definition of amenability, namely the existence of an invariant mean on the algebra of essentially bounded, measurable functions on the group.

Characterization of Class of Positive Lattice Measurable Sets and Positive Lattice Measurable Functions

2011 ◽  
Vol 5 (1) ◽  
pp. 43-51 ◽  
Author(s):  
J. Pramada ◽  
J. Venkateswara Rao ◽  
D.V.S.R. Anil Kumar
Keyword(s):  
Measurable Functions

Inextensible Riesz spaces

1975 ◽  
Vol 77 (1) ◽  
pp. 71-89 ◽  
Author(s):  
D. H. Fremlin
Keyword(s):  
Measurable Cardinal ◽  
Riesz Space ◽  
Abstract Characterization ◽  
Riesz Spaces ◽  
The Third ◽  
The Subject

My aim in this paper is to give an abstract characterization of the C∞ spaces described in (6) or (9), and to develop some of the remarkable special properties of these spaces. Although the subject is in some ways highly specialized, inextensible and sequentially inextensible spaces seem common enough (they include all spaces of the forms Rx and L0) to be worth studying, and I have already employed them in the proof of more general results (1).In the first section I set out those properties that can be described in simple Riesz space terms; much of this work has already been published in slightly different forms. In the second part I go on to questions that arise when we impose a topology on an inextensible Riesz space. Finally, in the third section, I discuss some problems, arising from the work before, which are related to the famous measurable cardinal problem.

Modes of ideal continuity and the additive property in the Riesz space setting

2014 ◽  
Vol 20 (1) ◽  
Author(s):  
Antonio Boccuto ◽  
Xenofon Dimitriou ◽  
Nikolaos Papanastassiou ◽  
Władysław Wilczyński
Keyword(s):  
Riesz Space ◽  
Ideal Convergence ◽  
Additive Property ◽  
Basic Properties ◽  
Space Setting ◽  
Comparison Results ◽  
Different Types

Abstract.In this paper we present some different types of ideal convergence/divergence and of ideal continuity for Riesz space-valued functions, and prove some basic properties and comparison results. We investigate the relations among different modes of ideal continuity and present a characterization of the (

scholarly journals Minimization of φ-divergences on sets of signed measures

2006 ◽  
Vol 43 (4) ◽  
pp. 403-442 ◽  
Author(s):  
Michel Broniatowski ◽  
Amor Keziou
Keyword(s):  
Probability Measure ◽  
Vector Space ◽  
Minimization Problem ◽  
Weak Topology ◽  
Linear Constraints ◽  
Measurable Functions ◽  
Class F

We consider the minimization problem of φ-divergences between a given probability measure P and subsets Ω of the vector space M F of all signed measures which integrate a given class F of bounded or unbounded measurable functions. The vector space M F is endowed with the weak topology induced by the class F ∪ B b where B b is the class of all bounded measurable functions. We treat the problems of existence and characterization of the φ-projections of P on Ω. We also consider the dual equality and the dual attainment problems when Ω is defined by linear constraints.

scholarly journals Quotient bounded elements in locally convex algebras

1982 ◽  
Vol 33 (1) ◽  
pp. 102-113 ◽  
Author(s):  
Subhash J. Bhatt
Keyword(s):  
Convex Space ◽  
Locally Convex Space ◽  
Linear Operators ◽  
Continuous Linear ◽  
Spatial Characterization ◽  
Measurable Functions ◽  
Locally Convex ◽  
Locally Convex Algebra ◽  
Continuous Linear Operators

AbstractThe quotient bounded and the universally bounded elements in a calibrated locally convex algebra are defined and studied. In the case of a generalized B*-algebra A, they are shown to form respectively b* and B*-algebras, both dense in A. An internal spatial characterization of generalized B*-algebras is obtained. The concepts are illustrated with the help of examples of algebras of measurable functions and of continuous linear operators on a locally convex space.

scholarly journals THE FATOU COMPLETION OF A FRÉCHET FUNCTION SPACE AND APPLICATIONS

2009 ◽  
Vol 88 (1) ◽  
pp. 49-60 ◽  
Author(s):  
R. DEL CAMPO ◽  
W. J. RICKER
Keyword(s):  
Function Space ◽  
Riesz Space ◽  
Fréchet Space ◽  
Frechet Space ◽  
Function Lattice ◽  
Measurable Functions ◽  
Integrable Functions ◽  
Locally Convex

AbstractGiven a metrizable locally convex-solid Riesz space of measurable functions we provide a procedure to construct a minimal Fréchet (function) lattice containing it, called its Fatou completion. As an application, we obtain that the Fatou completion of the space L1(ν) of integrable functions with respect to a Fréchet-space-valued measure ν is the space L1w(ν) of scalarly ν-integrable functions. Further consequences are also given.

scholarly journals On a Lindenbaum Composition Theorem

2019 ◽  
Vol 74 (1) ◽  
pp. 145-158
Author(s):  
Jaroslav Šupina ◽  
Dávid Uhrik
Keyword(s):  
Topological Space ◽  
Real Line ◽  
Topological Spaces ◽  
The Real ◽  
Measurable Functions ◽  
Borel Measurable ◽  
Composition Theorem ◽  
Perfectly Normal

Abstract We discuss several questions about Borel measurable functions on a topological space. We show that two Lindenbaum composition theorems [Lindenbaum, A. Sur les superpositions des fonctions représentables analytiquement, Fund. Math. 23 (1934), 15–37] proved for the real line hold in perfectly normal topological space as well. As an application, we extend a characterization of a certain class of topological spaces with hereditary Jayne-Rogers property for perfectly normal topological space. Finally, we pose an interesting question about lower and upper Δ02-measurable functions.

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