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Measurability of classes of Lipschitz manifolds with respect to Borel \(\sigma\)-algebra of Vietoris topology. (English) Zbl 1165.53304

Summary: The measurability of the classes of all \(k\)-dimensional Lipschitz manifolds with respects to the Borel \(\sigma\)-algebra of the Vietoris topology on the hyperspace of closed subsets of the \(d\)-dimensional Euclidean space is proved. By a \(k\)-dimensional Lipschitz manifold we understand a manifold without boundary locally representable by bi-Lipschitz images of closed half-spaces in \(\mathbb R^k\) or \(\mathbb R^k\) itself, respectively.

MSC:

53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
60D05 Geometric probability and stochastic geometry
58D10 Spaces of embeddings and immersions
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