Generalized convexity cones and their duals

Dan Amir and Zvi Ziegler

Vol. 27 (1968), No. 3, 425–440

DOI: 10.2140/pjm.1968.27.425

Abstract

The structure of the intersections and unions of generalized convexity cones is analysed. The main results involve on the one hand denseness properties of sums of two distinct generalized convexity cones and on the other hand the availability of a decomposition for measures of the cones dual to intersections of generalized convexity cones. As an application an integration scheme which converges for all convex functions is found.

Mathematical Subject Classification

Primary: 46.25

Secondary: 26.00

Milestones

Received: 1 August 1967

Published: 1 December 1968