Boolean Algebras : Reihe: Reelle Funktionen (Second Edition)

There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due t...

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Main Author: Sikorski, Roman
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1960, 1960
Edition:2nd ed. 1960
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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245 0 0 |a Boolean Algebras  |h Elektronische Ressource  |b Reihe: Reelle Funktionen (Second Edition)  |c by Roman Sikorski 
250 |a 2nd ed. 1960 
260 |a Berlin, Heidelberg  |b Springer Berlin Heidelberg  |c 1960, 1960 
300 |a X, 237 p  |b online resource 
505 0 |a Terminology and notation -- I. Finite joins and meets -- II. Infiinite joins and meets -- Append -- § 39. Relation to other algebras -- § 40. Applications to mathematical logic. Classical calculi -- § 41. Topology in Boolean algebras. Applications to non-classical logic -- § 42. Applications to measure theory -- § 43. Measurable functions and real homomorphisms -- § 44. Measurable functions. Reduction to continuous functions -- § 45. Applications to functional analysis -- § 46. Applications to foundations of the theory of probability -- § 47. Problems of effectivity -- List of symbols -- Author Index 
653 |a Mathematical Logic and Formal Languages 
653 |a Mathematical logic 
653 |a Functions of real variables 
653 |a Mathematics, general 
653 |a Real Functions 
653 |a Mathematics 
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490 0 |a Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics 
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520 |a There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the develop­ ment of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2J and HERMES [IJ. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No know­ ledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs