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An extreme simple proof of the K-K-M-S Theorem.
- Source :
- Economic Theory; 1997, Vol. 10 Issue 2, p361-367, 7p, 2 Diagrams
- Publication Year :
- 1997
-
Abstract
- An extremely simple proof of the K-K-M-S Theorem is given involving only Brouwer's fixed point theorem and some elementary calculus. A function is explicitly given such that a fixed point of it yields an intersection point of a balanced collection of sets together with balancing weights. Moreover, any intersection point of a balanced collection of sets together with balancing weights corresponds to a fixed point of the function. Furthermore, the proof can be used to show π-balanced versions of the K-K-M-S Theorem, with π-balancedness as introduced in Billera (1970). The proof makes clear that the conditions made with respect to π by Billera can be even weakened. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09382259
- Volume :
- 10
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Economic Theory
- Publication Type :
- Academic Journal
- Accession number :
- 4539511
- Full Text :
- https://doi.org/10.1007/s001990050161