Boolean Algebras in Analysis
Boolean Algebras in Analysis

Author: D.A. Vladimirov

Publisher: Springer Science & Business Media

Published: 2002-03-31

Total Pages: 630

ISBN-13: 9781402004803

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Boolean algebras underlie many central constructions of analysis, logic, probability theory, and cybernetics. This book concentrates on the analytical aspects of their theory and application, which distinguishes it among other sources. Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory. The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras, their sub algebras, and groups of automorphisms. Ample room is allotted to the new classification theorems abstracting the celebrated counterparts by D.Maharam, A.H. Kolmogorov, and V.A.Rokhlin. Boolean Algebras in Analysis is an exceptional definitive source on Boolean algebra as applied to functional analysis and probability. It is intended for all who are interested in new and powerful tools for hard and soft mathematical analysis.

Boolean Valued Analysis
Boolean Valued Analysis

Author: A.G. Kusraev

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 345

ISBN-13: 9401144435

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Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.

Analysis of Boolean Functions
Analysis of Boolean Functions

Author: Ryan O'Donnell

Publisher: Cambridge University Press

Published: 2014-06-05

Total Pages: 445

ISBN-13: 1107038324

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This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

Logic and Boolean Algebra
Logic and Boolean Algebra

Author: Bradford Henry Arnold

Publisher: Courier Corporation

Published: 2011-01-01

Total Pages: 163

ISBN-13: 0486483851

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Orignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962.

Introduction to Boolean Algebras
Introduction to Boolean Algebras

Author: Steven Givant

Publisher: Springer Science & Business Media

Published: 2008-12-10

Total Pages: 589

ISBN-13: 0387684360

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This book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.

Boolean Algebras in Analysis
Boolean Algebras in Analysis

Author: D.A. Vladimirov

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 614

ISBN-13: 940170936X

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Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory. The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras, their sub algebras, and groups of automorphisms. Ample room is allotted to the new classification theorems abstracting the celebrated counterparts by D.Maharam, A.H. Kolmogorov, and V.A.Rokhlin. Boolean Algebras in Analysis is an exceptional definitive source on Boolean algebra as applied to functional analysis and probability. It is intended for all who are interested in new and powerful tools for hard and soft mathematical analysis.

Lectures on Boolean Algebras
Lectures on Boolean Algebras

Author: Paul R. Halmos

Publisher: Courier Dover Publications

Published: 2018-09-12

Total Pages: 163

ISBN-13: 0486834573

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This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise and informal as well as systematic, the text draws upon lectures delivered by Professor Halmos at the University of Chicago to cover many topics in brief individual chapters. The approach is suitable for advanced undergraduates and graduate students in mathematics. Starting with Boolean rings and algebras, the treatment examines fields of sets, regular open sets, elementary relations, infinite operations, subalgebras, homomorphisms, free algebras, ideals and filters, and the homomorphism theorem. Additional topics include measure algebras, Boolean spaces, the representation theorem, duality for ideals and for homomorphisms, Boolean measure spaces, isomorphisms of factors, projective and injective algebras, and many other subjects. Several chapters conclude with stimulating exercises; the solutions are not included.

Introduction to the Comparative Method With Boolean Algebra
Introduction to the Comparative Method With Boolean Algebra

Author: Daniele Caramani

Publisher: SAGE

Published: 2009

Total Pages: 129

ISBN-13: 1412909759

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"Utilizing a systematic, broad approach, Introduction to the Comparative Method With Boolean Algebra gives readers the logical foundations of comparison with guided applications and is the ultimate comparative method text covering each of the current and most important issues in the field. Author Daniele Caramani discusses the elements of scientific research, including Mill's methods, Boolean algebra, classification and typologization, and necessary and sufficient conditions, and how these apply to concrete research in the social sciences." "This text is indispensable for upper-level undergraduate and graduate students as well as researchers interested in methodology, behavioral and social sciences, history, and logic."--BOOK JACKET.

Boolean Reasoning
Boolean Reasoning

Author: Frank Markham Brown

Publisher: Courier Corporation

Published: 2012-02-10

Total Pages: 308

ISBN-13: 0486164594

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Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.