Sets of asymptotic values of positive linear measure

Asymptotic Values of Vector Measure Games

The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v S of a coalition S is a function f of S where is a vector measure. Special classes of vector measure games are the weighted majority games and the two-house weighted majority games, where a tw...

Asymptotic Distribution of Divergence Measure with Applications

Families of Sets of Positive Measure

We present a combinatorial description of those families 5a of sets, for which there is a finite measure p. such that inf{ß{P) : P 6 a"} > 0 . This result yields a topological characterization of measure-compactness and Borel measure-compactness. It is also applied to a problem on the existence of regular measure extensions. The main part of this paper deals with the following problem. Given a ...

Homogeneous sets of positive outer measure∗

For every Polish space and a coanalytic set of its countable subsets, if there is a homogeneous set of outer measure one then there is a perfect homogeneous set. In the generic extension by a large measure algebra, if there is a homogeneous set of size continuum then there is a a perfect homogeneous set.

Asymptotic Lifts of Positive Linear Maps

We show that the notion of asymptotic lift generalizes naturally to normal positive maps φ : M → M acting on von Neumann algebras M . We focus on cases in which the domain of the asymptotic lift can be embedded as an operator subsystem M∞ ⊆ M , and characterize when M∞ is a Jordan subalgebra of M in terms of the asymptotic multiplicative properties of φ.