Games in Banach spaces
  The notion of Aronszajn-null sets generalizes the notion of Lebesgue measure zero on the real line and the Euclidean space to infinite dimensional Banach spaces.   We present a game-theoretic approach to Aronszajn-null sets, establish its basic properties, and discuss the ensuing open problems. 
Jakub Duda and Boaz Tsaban