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Further Properties of Additive Functions and Convex Functions

Abstract

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

Keywords

Convex Function Additive Function Pairwise Disjoint Positive Measure Measure Zero 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2009

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