Article contents
Ramsey type theorems for real functions
Published online by Cambridge University Press: 26 February 2010
Abstract
Ramsey's theorem implies that every function f:0, 1 ℝ isconvex or concave on an infinite set. We show that there is an upper semicontinuous function which is not convex or concave on any uncountable set. We investigate those functions which are not convex on any r element set (r ). A typical result: if f is bounded from below and is not convex on any infiniteset then there exists an interval on which the graph of f can be covered by the graphs of countably many strictly concave functions.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright University College London 1989
References
- 1
- Cited by