Further Properties of Additive Functions and Convex Functions
Let D ⊂ ℝN be a convex and open set, and let f : D → ℝ be a convex function. Let mf be the lower hull of f (cf. 6.3). By Theorem 6.3.1 either mf(x) = -∞ for all x ∈ D, or mf : D → ∝ is a continuous and convex function.
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