Skip to main content
×
Home
    • Aa
    • Aa

Measures of the non-convexity of sets and the Shapley–Folkman–Starr theorem

  • J. W. S. Cassels (a1)
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)).

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

(2)R. Starr Quasi-equilibria in markets with nonconvex preferences. Econometrics 37 (1969), 2538.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×