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Part of the book series: Studies in Economic Theory ((ECON.THEORY,volume 13))

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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

  • eBook Packages: Springer Book Archive

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