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October 11th, 2018, 05:05 AM  #1 
Newbie Joined: Nov 2013 Posts: 19 Thanks: 0  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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inequality, prove 
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