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 c X we mean a sublinear function p : X == R such that C = [p <= 1]. Besides the most important instance, namely the Minkowski gauge mC(x) = inf {l > 0 : x e lC}, the set C may have other gauges, which are...</=>