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A
representation theorem for real convex functions
Roy Martin Rakestraw |
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Vol. 60 (1975), No. 2, 165–168
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Abstract |
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The Krein-Milman theorem is used to prove the following result. A nonnegative function f on [0,1] convex if, and only if, there exist nonnegative Borel measures μ1 and μ2 on [0,1] such that ![∫ x −1 ∫ 1
f (x) = 0 (1 − ξ) (x− ξ)dμ1(ξ)+ x [1 − (x∕ξ)]dμ2(ξ),](a170x.png) for every x ∈ [0,1]. An example is given for which the representation is not unique. |
Mathematical Subject Classification 2000
Primary: 26A51
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Milestones
Received: 31 January 1974
Published: 1 October 1975
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Authors |
| Roy Martin Rakestraw | |
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