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Let $d\in\mathbb N$; $U\subseteq\mathbb R^d$ be open and $$\mathcal A:=\{\Omega\subseteq U:\Omega\text{ is bounded and open and }\partial\Omega\text{ is of class }C^{0,\:1}\};$$ $E:=\bigcup_{\Omega\...

Let $(M,g,m_0)$ be a pointed-Hadamard manifold with Riemmanian distance function $d_g$, $(X,\Sigma,\mu)$ be a finite measure space. We use $L^2(\mu;M,m_0)$ to denote the metric space consisting of ...