## 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

### Keywords:

Vietoris topology; Lipschitz manifolds
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