Bru, Bernard (Author)
Bru, Marie-France (Author)
Chung, Kai Lai (Author)
Thispaperexamines---bymeansoftheexampleoftheSt.Peters-burgparadox---howBorelexpositedthescienceofhisday.ThefirstpartsketchesthesingularplaceofpopularizationinBorel'swork.ThetwopartsthatfollowgiveachronologicalpresentationofBorel'scon-tributionstotheSt.Petersburgparadox,contributionsthatevolvedoveraperiodofmorethanfiftyyears.TheseshowhowBorelattackedtheproblembypositioningitinalong---andscientificallyveryrich---meditationontheparadoxofmartingales,thosesystemsofplaythatpurporttomakeagamblertossingacoinrich.Borelgaveanorigi-nalsolutiontothisproblem,anticipatingthefundamentalequalityofthenascentmathematicaltheoryofmartingales.TheparadoxicalroleplayedbyF'elixLeDantecinthedevelopmentofBorel'sthoughtonthesethemesishighlighted.AnappendixrecastsBorel'smartingalesinmodernterms.
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