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$\newcommand{\diff}{ \, \mathrm d}$ Let $X,Y$ be Polish spaces, $\mathcal C_b(X)$ the space of all real-valued bounded continuous functions on $X$, $\mathcal P(X)$ the space of Borel probability ...

Fix a positive integer $n$, let $\mathbb{H}^n$ be the $n$-dimensional hyperbolic space, $r>0$, $x\in \mathbb{H}^n$ and consider the closed (compact) geodesic ball $B_{\mathbb{H}^n}(x,r)$. Are ...