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024 7 10.1007/978-0-387-87857-7|2doi
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072 7 MAT015000|2bisacsh
082 04 510.9|223
100 1 Fischer, Hans.|eauthor.
245 12 A History of the Central Limit Theorem|h[electronic
resource] :|bFrom Classical to Modern Probability Theory /
|cby Hans Fischer.
260 1 New York, NY :|bSpringer New York,|c2011.
300 XVI, 402 p.|bonline resource.
338 online resource|bcr|2rdacarrier
347 text file|bPDF|2rda
490 1 Sources and Studies in the History of Mathematics and
490 0 Springer eBooks.|aMathematics and Statistics
505 0 Preface -- Introduction -- The central limit theorem from
laplace to cauchy: changes in stochastic objectives and in
analytical methods -- The hypothesis of elementary errors
-- Chebyshev's and markov's contributions -- The way
towards modern probability -- General limit problems --
Conclusion: the central limit theorem as a link between
classical and modern probability -- Index -- Bibliography.
520 This study aims to embed the history of the central limit
theorem within the history of the development of
probability theory from its classical to its modern shape,
and, more generally, within the corresponding development
of mathematics. The history of the central limit theorem
is not only expressed in light of "technical" achievement,
but is also tied to the intellectual scope of its
advancement. The history starts with Laplace's 1810
approximation to distributions of linear combinations of
large numbers of independent random variables and its
modifications by Poisson, Dirichlet, and Cauchy, and it
proceeds up to the discussion of limit theorems in metric
spaces by Donsker and Mourier around 1950. This self-
contained exposition additionally describes the historical
development of analytical probability theory and its tools,
such as characteristic functions or moments. The
importance of historical connections between the history
of analysis and the history of probability theory is
demonstrated in great detail. With a thorough discussion
of mathematical concepts and ideas of proofs, the reader
will be able to understand the mathematical details in
light of contemporary development. Special terminology and
notations of probability and statistics are used in a
modest way and explained in historical context.
650 0 Mathematics.
650 0 History.
650 0 Probabilities.
650 0 Statistics.
650 14 Mathematics.
650 24 History of Mathematical Sciences.
650 24 Probability Theory and Stochastic Processes.
650 24 Statistics, general.
710 2 SpringerLink (Online service)
773 0 |tSpringer eBooks
776 08 |iPrinted edition:|z9780387878560
830 0 Sources and Studies in the History of Mathematics and
856 40 |zAcceso al texto completo|uhttp://dx.doi.org/10.1007/978-
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