We introduce μ‐convexity, a new kind of game convexity defined on a σ‐algebra of a nonatomic finite measure space. We show that μ‐convex games are μ‐average monotone. Moreover, we show that μ‐average monotone games are totally balanced and their core contains a nonatomic finite signed measure. We apply the results to the problem of partitioning a measurable space among a finite number of individuals. For this problem, we extend some results known for the case of individuals’ preferences that are representable by nonatomic probability measures to the more general case of nonadditive representations.
