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The Splendors and Miseries of MartingalesAndrei Kolmogorov and Leonid Levin on Randomness

The Splendors and Miseries of Martingales: Andrei Kolmogorov and Leonid Levin on Randomness [This chapter provides a translation of a letter written in 1939, in which Andrei Kolmogorov’s explains his views on the connection between probability theory and its applications. It also provides some historical sources on the early history of Kolmogorov complexity in Russia (then the USSR): abstracts of talks by Kolmogorov and letters from Leonid Levin to Kolmogorov. The relation between Levin’s measures and semimeasures on the one hand and martingales and supermartingales on the other is explained in the present volume’s chapter “Martingales in the Study of Randomness”.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Splendors and Miseries of MartingalesAndrei Kolmogorov and Leonid Levin on Randomness

Part of the Trends in the History of Science Book Series
Editors: Mazliak, Laurent; Shafer, Glenn

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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
ISBN
978-3-031-05987-2
Pages
405 –414
DOI
10.1007/978-3-031-05988-9_19
Publisher site
See Chapter on Publisher Site

Abstract

[This chapter provides a translation of a letter written in 1939, in which Andrei Kolmogorov’s explains his views on the connection between probability theory and its applications. It also provides some historical sources on the early history of Kolmogorov complexity in Russia (then the USSR): abstracts of talks by Kolmogorov and letters from Leonid Levin to Kolmogorov. The relation between Levin’s measures and semimeasures on the one hand and martingales and supermartingales on the other is explained in the present volume’s chapter “Martingales in the Study of Randomness”.]

Published: Oct 18, 2022

Keywords: Andrei Kolmogorov; Complexity; Leonid Levin; Randomness; Semimeasure

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