Author : Michel Talagrand
Publisher : American Mathematical Soc.
Page : 238 pages
File Size : 48,32 MB
Release : 1984
Category : Banach spaces
ISBN : 0821823078
We present a self-contained account of measure theory and integration in a Banach space. We give a detailed analysis of the weak Baire probabilities on a Banach space E, and on its second dual. Scalarly (= weak) measurable functions valued in E are studied via their image measure and it is shown how to regularize them using lifting. General criteria are given to ensure that they are Pettis integrable. This study relies on tools from topological and abstract measure theory.
Author : Michel Talagrand
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 24,39 MB
Release : 1984-12-31
Category : Mathematics
ISBN : 9780821860465
Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 40,6 MB
Release : 2021-09-03
Category : Education
ISBN : 1470466406
This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author : E. Pap
Publisher : Elsevier
Page : 1633 pages
File Size : 42,82 MB
Release : 2002-10-31
Category : Mathematics
ISBN : 0080533094
The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.
Author : J.M. Belley
Publisher : Springer
Page : 335 pages
File Size : 39,37 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540386904
a
Author : Joseph Diestel
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 50,72 MB
Release : 1977-06-01
Category : Mathematics
ISBN : 0821815156
In this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces. A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems.
Author : D. H. Fremlin
Publisher : Torres Fremlin
Page : 967 pages
File Size : 47,36 MB
Release : 2000
Category : Fourier analysis
ISBN : 0953812944
Author : ?tefan Schwabik
Publisher : World Scientific
Page : 313 pages
File Size : 38,69 MB
Release : 2005
Category : Mathematics
ISBN : 9812564284
The relatively new concepts of the Henstock-Kurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The Henstock-Kurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.
Author : Guillermo Curbera
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 39,39 MB
Release : 2010-02-21
Category : Mathematics
ISBN : 3034602111
This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in thearea and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, andfunctional analysis. The material is of interest to experts, young researchers and postgraduate students.
Author : Library of Congress. Cataloging Policy and Support Office
Publisher :
Page : 1512 pages
File Size : 43,9 MB
Release : 2007
Category : Subject headings, Library of Congress
ISBN :
