On Relatively Nonatomic Measures
نویسنده
چکیده
منابع مشابه
CONTINUOUS VALUES OF MARKET GAMES ARE CONIC By
We prove that every continuous value on a space of vector measure market games Q, containing the space of nonatomic measures NA, has the conic property, i.e., if a game v ∈ Q coincides with a nonatomic measure ν on a conical diagonal neighborhood then φ(v) = ν. We deduce that every continuous value on the linear spaceM, spanned by all vector measure market games, is determined by its values on ...
متن کاملCounting Generic Measures for a Subshift of Linear Growth
In 1984 Boshernitzan proved an upper bound on the number of ergodic measures for a minimal subshift of linear block growth and asked if it could be lowered without further assumptions on the shift. We answer this question, showing that Boshernitzan’s bound is sharp. We further prove that the same bound holds for the, a priori, larger set of nonatomic generic measures, and that this bound remain...
متن کاملValues of smooth nonatomic games : the method of multilinear approximation
In their book Values of Non-Atomic Games, Aumann and Shapley [1] define the value for spaces of nonatomic games as a map from the space of games into bounded finitely additive games that satisfies a list of plausible axioms: linearity, symmetry, positivity, and efficiency. One ofthe themes of the theory of values is to demonstrate that on given spaces of games this list of plausible axioms dete...
متن کاملOptimal-partitioning Inequalities for Nonatomic Probability Measures
Suppose fix,... ,fin are nonatomic probability measures on the same measurable space (S, S). Then there exists a measurable partition isi}"=i of 5 such that Pi(Si) > (n + 1 M)'1 for a11 i l,...,n, where M is the total mass of V?=i ßi (tne smallest measure majorizing each m). This inequality is the best possible for the functional M, and sharpens and quantifies a well-known cake-cutting theorem ...
متن کاملA new class of convex games on σ-algebras and the optimal partitioning of measurable spaces
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 indiv...
متن کامل