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Mat. Sb., 2008, Volume 199, Number 11, Pages 21–44 (Mi msb3948)  

This article is cited in 1 scientific paper (total in 1 paper)

Lebesgue measure and gambling

V. G. Kanoveia, T. Lintonb, V. A. Uspenskiic

a Institute for Information Transmission Problems, Russian Academy of Sciences
b Central College
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Lebesgue measure of point sets is characterized in terms of the existence of various strategies in a certain coin-flipping game. ‘Rational’ and ‘discrete’ modifications of this game are investigated. We prove that if one of the players has a winning strategy in a game of this type depending on a given set $P\subseteq[0,1]$, then this set is measurable.
Bibliography: 11 titles.

DOI: https://doi.org/10.4213/sm3948

Full text: PDF file (616 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:11, 1597–1619

Bibliographic databases:

UDC: 510.225+517.518.112
MSC: Primary 28A05; Secondary 03E15, 03E60
Received: 27.09.2007 and 02.07.2008

Citation: V. G. Kanovei, T. Linton, V. A. Uspenskii, “Lebesgue measure and gambling”, Mat. Sb., 199:11 (2008), 21–44; Sb. Math., 199:11 (2008), 1597–1619

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Osoinach J.K., Phillips D.P., “The infinite duration lying oracle game”, Optimization, 63:3 (2014), 459–471  crossref  mathscinet  zmath  isi  elib  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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