Abstract: This chapter is devoted to a class of functions from ℝ n into ℝ∪ +∞ called convex functions and to give a first important property of such functions. Any convex function is continuous on the interior of its domain if this one is nonempty. If the domain of a convex function f has an empty interior, then the restriction of f to the affine set spanned by its domain is continuous on the relative interior of its domain (this expression makes sense because the domain of a convex function is a convex set).
Publication Year: 2001
Publication Date: 2001-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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