Some Applications of a Theorem on Convex Functions

by Samuel Karlin, Lloyd S. Shapley

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This note presents several applications of the theory developed elsewhere by the authors and H. F. Bohnenblust. The results established here depend upon fundamental theorem on convex functions, previously used in relation to the Theory of Games. Certain extensions of Helly's theorem, approximation and fitting results, and covering theorems for the n dimensional unit sphere are obtained. All these are intrinsically connected with one another. The authors believe they possess independent interest.

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