Intrinsic entropies of log-concave distributions.

The entropy of a random variable is well-known to equal the exponential growth rate of the volumes of its typical sets. In this paper, we show that for any log-concave random variable X, the sequence of the [nθ]th intrinsic volumes of the typical sets of X in dimensions n ≥ 1 grows exponentially with a well-defined rate. We denote this rate by hX (θ), and call it the θth intrinsic entropy of X. We...