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I was reading the article by Tom Leinster, (Maximizing diversity in biology and beyond, arXiv link), and find it very interesting. Since I was searching for entropies of finite metric spaces I found ...

Let $\mathcal{P}(\mathbb{R}^d)$ the space of probability measures on $\mathbb{R}^d$ with total variation metric $\delta$, fix $k \in \mathbb{N}$, and let $\mathcal{P}'\subset \mathcal{P}(\mathbb{R}^d)$...