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- Jun 20, 2014

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Let $\Lambda :\Bbb R \to \Bbb R$ be a mapping such that for all bounded measurable mappings $f : [0,1]\to \Bbb R$,

$$\Lambda\left(\int_0^1 f(x)\, dx\right) \le \int_0^1 \Lambda(f(x))\, dx.$$

Show that $\Lambda$ is a convex mapping.

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