# 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.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics