Representations of Real Numbers by Infinite Series
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502 J&nos Galambos
Representations of Real Numbers by Infinite Series m
Springer-Verlag Berlin. Heidelberg
!
New 9 York 1976
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Author Prof..htnos Galambos Department of Mathematics Temple University Philadelphia, PA 19121 USA
Library of Congress Cataloging in Publication Data
Galambos, J~nos, 1940Representations of real numbers by infinite series. (Lecture notes in mathematics ; 502) ~i bli ogTaphy : p. Includes index. i. Numbers, ~heory of. 2. Numbers, Real. 3. Series, Infinite. I. Title. II. Series: Lecture notes in mathematics (Berlin) ; 502. QA~.L28 no.50e [q~2kl] 5ZO'.8s [512'.7]
75-~-4296
AMS Subject Classifications (1970): 10-02, 10A30,10 F35,10 K05,10 K10, 10K25 ISBN 3-540-07547-X Springer-V~rlag Berlin Heidelberg 9 N 9 ewYork ISBN 0-387-07547-X Springer-Verlag New York Heidelberg 9 Berlin 9 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under s 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. 9by Springer-Verlag Berlin Heidelberg 9 1976 Printed in Germany Offsetdruck: Julius Beltz, Hemsbach/Bergstr.
Acknowledgement
This
work
Leave
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tion,
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thanks
1974-75
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appreciated.
am Main, 1975
Janos
Galambos
Grohe
Content Introduction The Algorithms
4
1.1.
A
4
3.2.
The
Cantor
1.3.
The
Oppenheim
1.4.
The B a l k e m a - O p p e n h e i m
Chapter
Chapter
I:
II:
general
algorithm series
Questions Cantor's
2.2.
The
2.3.
Miscellaneous
III:
series
Concepts
and T o o l s
3.2.
Borel-Cantelli
3-3-
Laws
of
3.4.
Weak
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