Accession Number:

AD0758656

Title:

Some Properties of Orderable Set-Functions

Descriptive Note:

Technical rept.

Corporate Author:

STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH

Personal Author(s):

Report Date:

1972-10-01

Pagination or Media Count:

48.0

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 vJ vJ. 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 vs, 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.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE