Abstract
This chapter is devoted to a class of functions from ℝn 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).
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© 2001 Springer-Verlag Berlin Heidelberg
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Florenzano, M., Le Van, C. (2001). Convex Functions. In: Finite Dimensional Convexity and Optimization. Studies in Economic Theory, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56522-9_5
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DOI: https://doi.org/10.1007/978-3-642-56522-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62570-1
Online ISBN: 978-3-642-56522-9
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