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Given a compactly supported probability measure $m$ on $\mathbb{R}^n$, we can define its average distance to a point $x$ as $\int_\mathbb{R^n}d(x,y)dm(y)$. In this question I found that for a given ...

It is classical that Euclidean normal currents are dense in the space of all currents. This can be achieved through mollification. What I want to know if this is still true for metric currents. In ...

Fix $c>1$. Let $(X,d)$ be a separable compact metric space, does there necessarily exist a Borel probability measure $\nu$ on $(X,d)$ such that $\operatorname{sup}_{x \in X,r>0}\frac{\nu(\...