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
Distribution Statement : APPROVED FOR PUBLIC RELEASE