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## Details

Genre/Form: | Electronic books History |
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Additional Physical Format: | Print version: Von Plato, Jan. Creating modern probability. Cambridge [England] ; New York : Cambridge University Press, 1994 (DLC) 93019026 (OCoLC)27811683 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Jan Von Plato |

ISBN: | 9780511609107 0511609108 |

OCLC Number: | 817934399 |

Description: | 1 online resource (x, 323 pages). |

Contents: | 1. 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 -- 2. 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 -- 3. 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 -- 4. 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 -- 5. 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 -- 6. 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 -- 7. 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 -- 8. 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. 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. |

Series Title: | Cambridge studies in probability, induction, and decision theory. |

Responsibility: | Jan von Plato. |

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### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

'... von Plato has consulted and drawn on a substantial body of archival material: letters, unpublished manuscripts, and drafts of later-published papers. Thus his book does not just (as is sometimes the case) simply revisit the standard chestnuts of the field, but substantially adds to our knowledge of them ... In sum, this is a welcome addition to the literature: timely, informed, and technically competent.' Isis "The reader will find a wealth of interesting material in this book. Exploring the ways in which the investigation of initially disparate special cases in physics and mathematics eventually led to the development of unified, rigorous, general, and profound theories of formal probability and its application to the worlds of physics and the theory of action is a fascinating intellectual journey." Lawrence Sklar, The Journal of Philosophy "Von Plato's narrative...nicely interweaves the philosophical, historical, and mathematical aspects of the subject. In doing so von Plato has consulted and drawn on a substantial body of archival material: letters, unpublished manuscripts, and drafts of later-published papers. Thus his book does not just simply revisit the standard chestnuts of the field, but substantially adds to our knowledge of them....In sum, this is a welcome addition to the literature: timely, informed, and technically competent." S.L. Zabell, Isis "Von Plato's narrative...nicely interweaves the philosophical, historical, and mathematical aspects of the subject. In doing so von Plato has consulted and drawn on a substantial body of archival material: letters, unpublished manuscripts, and drafts of later-published papers. Thus his book does not just simply revisit the standard chestnuts of the field, but substantially adds to our knowledge of them....In sum, this is a welcome addition to the literature: timely, informed, and technically competent." S.L. Zabell, Isis "Jan von Plato's Creating Modern Probability is a book to celebrate. It will be a source of pleasure for probabilists and a stimulus for historians. Combing a sweeping vision with a sympathetic and thorough marshaling of sources, it brings to life the emergence of measure-theoretic probability in the first third of the twentieth century....Von Plato's mathematical precision will satisfy specialits, while his success in organizing his sources with respect to larger questions will provoke and enable a new cycle of historical research and debate.... With grace and finesse, von Plato has conquered the buffer period of 1900-1933 for history. With grace, because his understanding of the mathematics of the period cannot be faulted. With finesse, because he has honored fully the claims of contemporary probabilists." Glen Shafer, The Annals of Probability "Jan von Plato's Creating Modern Probability is a book to celebrate. It will be a source of pleasure for probabilists and a stimulus for historians. Combing a sweeping vision with a sympathetic and thorough marshaling of sources, it brings to life the emrgence of measure-theoretic probability in the first third of the twentieth century....Von Plato's mathematical precision will satisfy specialits, while his success in organizing his sources with respect to larger questions will provoke and enable a new cycle of historical research and debate.... With grace and finesse, von Plato has conquered the buffer period of 1900-1933 for history. With grace, becuase his understanding of the mathematics of the period cannot be faulted. With finesse, because he has honored fully the claims of contemporary probabilists." Glen Shafer, The Annals of Probability Read more...

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