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Foundations Of The Theory Of Probability by Andrei Nikolaevich Kolmogorov

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1The Logic Of Chance : An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Logical Bearings And Its Application To Moral And Social Science, And To Statistics

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2The Logic Of Chance : An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Logical Bearings Ant Its Application To Moral And Social Science

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3The Theory Of Probability, An Inquiry Into The Logical And Mathematical Foundations Of The Calculus Of Probability

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4The Logic Of Chance. An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Application To Moral And Social Science

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5The Logic Of Chance : An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Logical Bearings And Its Application To Moral And Social Science, And To Statistics

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6The Theory Of Probability, An Inquiry Into The Logical And Mathematical Foundations Of The Calculus Of Probability

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7The Logic Of Chance. An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Application To Moral And Social Science

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8The Logic Of Chance. An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Logical Bearings And Its Application To Moral And Social Science

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9Foundations Of The Theory Of Probability

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The purpose of this monograph is to give an axiomatic foundation for the theory of probability. The author set himself the task of putting in their natural place, among the general notions of modern mathematics, the basic concepts of probability theory—concepts which until recently were considered to be quite peculiar. This task would have been a rather hopeless one before the introduction of Lebesgue’s theories of measure and integration. However, after Lebesgue’s publication of his investigations, the analogies between measure of a set and probability of an event, and between integral of a function and mathematical expectation of a random variable, became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be in complete analogy with the corresponding properties of orthogonal functions. But if probability theory was to be based on the above analogies, it still was necessary to make the theories of measure and integra­ tion independent of the geometric elements which were in the foreground with Lebesgue. This has been done by Frechet. While a conception of probability theory based on the above general viewpoints has been current for some time among certain mathematicians, there was lacking a complete exposition of the whole system, free of extraneous complications.  I wish to call attention to those points of the present exposition which are outside the above-mentioned range of ideas familiar to the specialist. They are the following: Probability distributions in infinite-dimensional spaces (Chapter III, § 4) ; differentiation and integration of mathematical expectations with respect to a parameter (Chapter IV, § 5) ; and especially the theory of condi­ tional probabilities and conditional expectations (Chapter V). It should be emphasized that these new problems arose, of neces­sity, from some perfectly concrete physical problems. The sixth chapter contains a survey, without proofs, of some results of A. Khinchine and the author of the limitations on the applicability of the ordinary and of the strong law of large num­ bers. The bibliography contains some recent works which should be of interest from the point of view of the foundations of the subject.

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10The Logic Of Chance. An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Application To Moral And Social Science

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11The Logic Of Chance. An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Logical Bearings And Its Application To Moral And Social Science

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12The Logic Of Chance. An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Application To Moral And Social Science

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13The Logic Of Chance. An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Logical Bearings And Its Application To Moral And Social Science

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2nd ed., re-written and greatly enlarged

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14Foundations Of The Theory Of Probability

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16The Logic Of Chance. An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Logical Bearings And Its Application To Moral And Social Science

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17The Logic Of Chance, 3rd Edition An Essay On The Foundations And Provice Of The Theory Of Probability

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Book from Project Gutenberg: The Logic of Chance, 3rd edition An Essay on the Foundations and Provice of the Theory of Probability

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18The Logic Of Chance: An Essay On The Foundations And Nature Of The Theory Of Probability

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The Logic of Chance is a groundbreaking work in probability theory, written by logician John Venn, best known for his contributions to statistics and epistemology. Though not directly theological, this book was often cited in discussions of divine providence, free will, and the apparent randomness in the natural world, especially in debates over miracles and divine intervention. This edition preserves Venn’s rigorous treatment of chance, causality, and empirical reasoning, making it a bridge between science and philosophy.

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19The Logic Of Chance; An Essay On The Foundations And Province Of The Theory Of Probability, With Especial Reference To Its Logical Bearings And Its Application To Moral And Social Science, And To Statistics

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1Foundations of the theory of probability

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  • Title: ➤  Foundations of the theory of probability
  • Authors:
  • Language: English
  • Number of Pages: Median: 91
  • Publisher: ➤  Dover Publications, Incorporated - Chelsea Publishing Company - Creative Media Partners, LLC
  • Publish Date:
  • Publish Location: New York, USA

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  • First Year Published: 1950
  • Is Full Text Available: Yes
  • Is The Book Public: Yes
  • Access Status: Public

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