03005nmm a2200325 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002000139245010800159250001700267260006300284300003000347505062100377653004400998653002301042653003201065653002501097653001901122653001601141710003401157041001901191989003801210490010601248856007201354082001001426520124301436EB000685496EBX0100000000000000053857800000000000000.0cr|||||||||||||||||||||140122 ||| eng a97836620150701 aSikorski, Roman00aBoolean AlgebrashElektronische RessourcebReihe: Reelle Funktionen (Second Edition)cby Roman Sikorski a2nd ed. 1960 aBerlin, HeidelbergbSpringer Berlin Heidelbergc1960, 1960 aX, 237 pbonline resource0 aTerminology 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 aMathematical Logic and Formal Languages aMathematical logic aFunctions of real variables aMathematics, general aReal Functions aMathematics2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aErgebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics uhttps://doi.org/10.1007/978-3-662-01507-0?nosfx=yxVerlag3Volltext0 a515.8 aThere 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