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### Lipschitz-regularity of partition of unity

For convenience write $$\phi_U(x) = \| x - (K-U)\|.$$ Let $N = |\mathcal{U}|$ the number of open sets in the cover. Define  f_1(x) = \frac{1}{N} \sum \phi_U(x), \qquad f_2(x) = \left( \frac1N \sum ...
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The definition of a Gaussian process is as follows. A stochastic process $X(t), t \in T$ is a Gaussian process if for all $n \in \mathbb{N}$, $a_i \in \mathbb{R}$, $t_i \in T$, \$\sum_{i=1}^n a_i X(...