Abstract
We have already seen that linear functions are always continuous. More generally, a remarkable feature of convex functions on E is that they must be continuous on the interior of their domains. Part of the surprise is that an algebraic/geometric assumption (convexity) leads to a topological conclusion (continuity). It is this powerful fact that guarantees the usefulness of regularity conditions like Adom f ∩ cont g ≠ ∅ (3.3.9), which we studied in the previous section.
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© 2000 Springer Science+Business Media New York
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Borwein, J.M., Lewis, A.S. (2000). Convex Analysis. In: Convex Analysis and Nonlinear Optimization. CMS Books in Mathematics / Ouvrages de mathématiques de la SMC. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-9859-3_4
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DOI: https://doi.org/10.1007/978-1-4757-9859-3_4
Publisher Name: Springer, New York, NY
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