UID:
almafu_9960119234002883
Umfang:
1 online resource (x, 323 pages) :
,
digital, PDF file(s).
ISBN:
1-316-04559-5
,
0-511-60910-8
Serie:
Cambridge studies in probability, induction and decision theory
Inhalt:
This is the only book to chart the history and development of modern probability theory. It shows how in the first thirty years of this century probability theory became a mathematical science. The author also traces the development of probabilistic concepts and theories in statistical and quantum physics. There are chapters dealing with chance phenomena, as well as the main mathematical theories of today, together with their foundational and philosophical problems. Among the theorists whose work is treated at some length are Kolmogorov, von Mises and de Finetti. The principal audience for the book comprises philosophers and historians of science, mathematicians concerned with probability and statistics, and physicists. The book will also interest anyone fascinated by twentieth-century scientific developments because the birth of modern probability is closely tied to the change from a determinist to an indeterminist world-view.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover -- Half-title -- Series-title -- Title -- Copyright -- Contents -- Preface -- Introduction -- 1.1 What this book is all about -- 1.2 Shift from classical probability -- 1.3 Physics -- 1.4 The final stage, 1919-1933 -- Pathways to modern probability -- 2.1 First steps in measure theoretic probability. Axiomatization -- 2.2 Borel and the intrinsic properties of reals -- 2.3 Strong laws of large numbers -- 2.4 Continuous distribution problems. Weyl's view of causality -- Probability in statistical physics -- 3.1 Concepts of probability in classical statistical physics -- 3.2 Ergodic theory -- 3.3 Einstein's views on probability -- 3.4 Brownian motion and random processes -- 3.5 Radioactivity before its explanation in quantum theory -- Quantum mechanical probability and indeterminism -- 4.1 Probability in the old quantum theory -- 4.2 The probabilistic interpretation of quantum mechanics -- 4.3 The uncertainty relation -- Classical embeddings of probability and chance -- 5.1 Subjective or objective probability: a philosophical debate -- 5.2 The early phase of a theory of objective probability -- 5.3 The theory of Hopf -- Von Mises' frequentist probabilities -- 6.1 Mechanics, probability, and positivism -- 6.2 Foundations of probability: the theory of random sequences -- 6.3 A purely probabilistic physics -- 6.4 The fate of collectives -- Kolmogorov's measure theoretic probabilities -- 7.1 Foundations and philosophy of mathematics -- 7.2 The meaning of probability. Earliest results -- 7.3 Random processes and statistical physics -- 7.4 The Grundbegriffe -- 7.5 The curious reappraisal of von Mises' theory -- De Finetti's subjective probabilities -- 8.1 'Probability does not exist' -- 8.2 Exchangeability and the representation theorem -- 8.3 Stochastic processes: the renunciation of determinism -- 8.4 Foundations for the theory of probability.
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8.5 The problem of denumerable additivity -- Supplement: Nicole Oresme and the ergodicity of rotations -- 1 The question of the periodicity of the universe -- 2 The density of rotations of a circle by an irrational angle -- 3 Frequentist probability -- Bibliography -- Index of Names -- Index of Subjects.
,
English
Weitere Ausg.:
ISBN 0-521-59735-8
Weitere Ausg.:
ISBN 0-521-44403-9
Sprache:
Englisch
URL:
Volltext
(lizenzpflichtig)
URL:
https://doi.org/10.1017/CBO9780511609107
URL:
https://doi.org/10.1017/CBO9780511609107
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