Chebyshev's lectures on the theory of probability
type: Item
instance of: scholarly article
title: Chebyshev's lectures on the theory of probability
zbMATH Open document ID: 0796.01012
DOI: 10.1007/BF00375639
published in: Archive for History of Exact Sciences
publication date: 1994-06-29T00:00:00Z
review text: There exist three extant versions of P. N. Chebyshev's lecture notes: the manuscript by A. M. Lyapunov at the archive in Moscow, and also in a printed version edited in 1936 by A. N. Krylov, (the latter being unfortunately corrupted by misprints), a second much more detailed one in 1876/78 by N. A. Artemiev, discovered as late as 1986 in a Petersburg library, and a third (condensed) copy written down by A. A. Markov, kept in the Archive of Petersburg. Chebyshev regarded the theory of probability as a purely mathematical discipline, and declared that the propositions of the theory should be proved rigorously. He played his part in discovering the Bienaymé-Chebyshev-inequality, he made considerable progress in the most important topics of the theory: the generalization of the law of large numbers and the central limit theorem, he substantially broadened the field of stochastic research, he studied a certain class of dependent variables and made full use of the concept of random quantities (= the Russian equivalent of random variables). Chebyshev's lectures were easily understood by his pupils. Several hints are given to some recent publications concerning his life and work by Yu. A. Prochorov (1986), I. A. Golovinsky (1986), and that by T. L. Butzer and F. Jongmans (1989) about his western contacts. 44 references.
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 60-03
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 597686
zbMATH Keywords: Bienaymé-Chebyshev-inequality
zbMATH Keywords: central limit theorem
zbMATH Keywords: law of large numbers
zbMATH Keywords: random variables
author: O. B. Sheĭnin
reviewed by: Hilmar Grimm
MaRDI profile type: Publication
cites work: P. L. Chebyshev (1821-1894) and his contacts with Western European scientists
cites work: Q3351332
cites work: Q3783249
cites work: Studies in the History of Probability and Statistics. XXV. On the history of some statistical laws of distribution
cites work: Early history of the theory of probability
cites work: On the history of the statistical method in astronomy
cites work: A. A. Markov's work on probability
full work available at URL: https://doi.org/10.1007/bf00375639
OpenAlex ID: W2025201541
description: scientific article; zbMATH DE number 597686