On Subgradients of Convex Functions and Orlicz Pseudo-Norms for Vector-Valued Functions

We discuss variants of construction of measurable subgradients for multivariate convex functions and the problem of characterization of the ${\mathrm{\Delta }}_2$-condition in terms of their directional derivatives. Furthermore we study related basic properties of Luxemburg and Orlicz pseudo-norms for vector-valued functions.