A History of the Central Limit Theorem From Classical to Modern Prob
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
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J.Z. Buchwald Associate Editors
J.L. Berggren and J. Lützen Advisory Board
C. Fraser, T. Sauer, A. Shapiro
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Hans Fischer
A History of the Central Limit Theorem From Classical to Modern Probability Theory
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Hans Fischer Katholische Universität Eichstätt-Ingolstadt Mathematisch-Geographische Fakultät D-85072 Eichstätt Germany [email protected]
ISBN 978-0-387-87856-0 e-ISBN 978-0-387-87857-7 DOI 10.1007/978-0-387-87857-7 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010935663 Mathematics Subject Classification (2010): Primary: 60-03; Secondary: 01A55, 01A60, 26-03, 42-03, 60F05, 62-03 c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This book is an entirely revised, in some parts considerably shortened, in other parts enlarged, version of a study which was originally published in German with the title “Die verschiedenen Formen und Funktionen des zentralen Grenzwertsatzes in der Entwicklung von der klassischen zur modernen Wahrscheinlichkeitsrechnung” at Shaker Verlag (Aachen, Germany) in 2000. I thank Shaker for giving me the permission to republish large parts of that work in an English translation. This mainly concerns chapters 1, 3, 4, and 5 of the present book. Most parts of this book have been translated from German or directly written in English by the author himself, except for chapters 1 and 8, as well as the first part of chapter 5 up to section 5.1.2 inclusively, section 6.1, and section 7.2, which were translated by Gavin Bruce from the author’s German drafts. Brent Runyan and Andreas Ellwanger corrected those portions of text which are less mathematical. During the long time of preparing the original and thereafter the present version of the book, many people gave me assistance and advice. As representative of all the persons who considerably helped me with the 2000 book, I thank Ivo Schneider in the first place for his comprehensive and continuous support. Ulrich Oppel kindly gave many valuable hints about mathematical details. The idea to publish an English version was primarily inspired by Reinhard Siegmund-Schultze, and I thank him very much
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