Lebesgue measure and gambling
Vladimir Grigor'evich Kanovei, Том Линтон, Vladimir Uspensky · Sbornik Mathematics · 2008
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 , then this set is measurable. Bibliography: 11 titles.