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- Published 2017 in ArXiv

<lb>The entropy of a random variable is well-known to equal the exponential growth rate of the<lb>volumes of its typical sets. In this paper, we show that for any log-concave random variable<lb>X , the sequence of the ⌊nθ⌋th intrinsic volumes of the typical sets of X in dimensions n ≥ 1<lb>grows exponentially with a well-defined rate. We denote this rate by hX(θ), and call it the θ th<lb>intrinsic entropy of X . We show that hX(θ) is a continuous function of θ over the range [0, 1],<lb>thereby providing a smooth interpolation between the values 0 and h(X) at the endpoints 0 and<lb>1, respectively.<lb>

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@article{Jog2017IntrinsicEO,
title={Intrinsic entropies of log-concave distributions},
author={Varun Jog and Venkat Anantharam},
journal={CoRR},
year={2017},
volume={abs/1702.01203}
}