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October 11th, 2018, 06:05 AM   #1
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Unhappy Prove an inequality.

Given that $\textstyle\sum_x2^{-H\left(x\right)}<1$, prove that $-{\textstyle\sum_x}p\left(x\right)\log p\left(x\right)<{\textstyle\sum_x}p\left(x\right)H \left(x\right)$. $p\left(x\right)$ is a distribution. $H\left(x\right)$ is always greater than 1.
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