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An extension theorem for convex functions and an application to Teicher's characterization of the normal distribution
Published online by Cambridge University Press: 26 February 2010
Extract
The main aim of this note is the proof of the following
Let −∞ ≤ a > b ≤ ∞ and let A ⊂ (a, b) be a measurable set such that λ((a, b)\A) = 0, where λ denotes Lebesgue measure on ℝ. Let f: A→ℝ be a measurable and midconvex function, i.e.
whenever. Then there exists a convex functionsuch that.
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- Research Article
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- Copyright © University College London 1987