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140122 ||| eng |
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|a 9783662015070
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|a Sikorski, Roman
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| 245 |
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|a Boolean Algebras
|h Elektronische Ressource
|b Reihe: Reelle Funktionen (Second Edition)
|c by Roman Sikorski
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| 250 |
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|a 2nd ed. 1960
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 1960, 1960
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| 300 |
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|a X, 237 p
|b online resource
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|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
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| 653 |
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|a Functions of real variables
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| 653 |
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|a Formal Languages and Automata Theory
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| 653 |
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|a Machine theory
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| 653 |
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|a Real Functions
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| 653 |
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|a Mathematics
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
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| 028 |
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|a 10.1007/978-3-662-01507-0
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| 856 |
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|u https://doi.org/10.1007/978-3-662-01507-0?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515.8
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| 520 |
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|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 latticetheory 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
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