Geodesic
Lebesgue measure and gambling
Sbornik. Mathematics, Tome 199 (2008) no. 11, pp. 1597-1619 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. G. Kanovei; T. Linton; V. A. Uspenskii. Lebesgue measure and gambling. Sbornik. Mathematics, Tome 199 (2008) no. 11, pp. 1597-1619. http://geodesic.mathdoc.fr/item/SM_2008_199_11_a1/

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