Accession Number : AD0660036

Title :   MEASURABLE UTILITY AND THE MEASURABLE CHOICE THEOREM.

Descriptive Note : Research memo.,

Corporate Author : HEBREW UNIV JERUSALEM (ISRAEL) DEPT OF MATHEMATICS

Personal Author(s) : Aumann,Robert J.

Report Date : AUG 1967

Pagination or Media Count : 24

Abstract : Three theorems are proved that are useful in mathematical treatments of economic models with a continuum of economic agents. The first, called the measurable choice theorem, gives conditions under which it is possible to find a measurable point-valued function whose graph is included in the graph of a given set-valued function whose graph is measurable. The second theorem concerns conditions under which the projection of a measurable set is measurable. Both these theorems generalize known theorems on these subjects. The third theorem treats a situation in which the set of economic agents forms a measure space, and each agent t has preference order on some space of outcomes; conditions are given under which it is possible to define a utility function for each trader which will be measurable as a function of the trader. (Author)

Descriptors :   (*ECONOMICS, MATHEMATICAL MODELS), (*MEASURE THEORY, ECONOMICS), SET THEORY, TOPOLOGY, THEOREMS

Subject Categories : Economics and Cost Analysis
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE