Convex radiant costarshaped sets and the least sublinear gauge

摘要

The paper studies convex radiant sets(i.e. containing the origin)of a linear normed space X and their representation by means of a gauge. By gauge of a convex radiant set C ? X we mean a sublinear function p: X → ? such that C = [p ≤ 1]. Besides the most important instance, namely the Minkowski gauge μc(x)= inf{λ > 0: x ∈ λC