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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. 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
347    text file|bPDF|2rda 
490 1  Sources and Studies in the History of Mathematics and 
       Physical Sciences 
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 
       Physical Sciences 
856 40 |zAcceso al texto completo|uhttp://dx.doi.org/10.1007/978-
       0-387-87857-7