Measures of the non-convexity of sets and the Shapley–Folkman–Starr theorem
- 1 November 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 78 (3) , 433-436
- https://doi.org/10.1017/s0305004100051884
Abstract
The object of this note is to show that elementary probability considerations suggest a very natural way of measuring the non-convexity of a set in euclidean space or, more generally, in a real Hilbert space . In particular they give a proof, much simpler and under less restrictive conditions, of results due to Shapley, Folkman and Starr which are of importance in Mathematical Economics ((1),(2)).Keywords
This publication has 1 reference indexed in Scilit:
- Quasi-Equilibria in Markets with Non-Convex PreferencesEconometrica, 1969