Abstract
Abstract : A set function (not necessarily additive) on a measurable space I is called orderable if for each measurable order (Aumann, R. J. and L. S. Shapley, Values of Non-atomic games, Princeton University Press, Princeton, 1973), K on I there is a measure phi sup R on I such that for all subsets J of I that are initial segments phi sup R v(J) = v(J). Properties like non-atomicity, nullness of sets and weak continuity are shown to be inherited from orderable set functions v to the phi sup R v's, and vice versa. A characterization of set functions which are absolutely continuous (w.r.t. some positive measure) in the set of orderable set functions is also given.
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