Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published April 1997 | public
Journal Article

On Independence for Non-Additive Measures, with a Fubini Theorem

Abstract

An important technical question arising in economic and financial applications of decision models with non-additive beliefs is how to define stochastic independence. In fact the straightforward generalization of independence does not in general yield a unique product. I discuss the problem of independence, with specific focus on the validity of the Fubini theorem. The latter holds in general only for a special class of functions. It also requires a stronger notion of independent product. This is unique when the product must be a belief function. Finally I discuss an application to the issue of randomization in decision making.

Additional Information

© 1997 Academic Press. Received 3 May 1995, Revised 21 June 1996. This paper is a modified version of Chapter 4 of my doctoral dissertation at UC Berkeley. I thank my adviser Bob Anderson, Massimo Marinacci, Klaus Nehring, Chris Shannon, and especially Marco Scarsini for helpful comments and discussion. Detailed comments from a referee and an associate editor greatly helped making this paper leaner. The usual disclaimer applies. Financial support from an Alfred P. Sloan Doctoral Dissertation Fellowship is gratefully acknowledged.

Additional details

Created:
August 19, 2023
Modified:
October 17, 2023