MEASURABLE UTILITY AND THE MEASURABLE CHOICE THEOREM.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1967
- Accession Number
- AD0660036
Entities
People
- Robert J. Aumann
Organizations
- Hebrew University of Jerusalem