Alpha sets in finite-dimensional euclidean spaces and their properties

@article{Ushakov2017AlphaSI,
  title={Alpha sets in finite-dimensional euclidean spaces and their properties},
  author={Vladimir N. Ushakov and Aleksandr A. Uspenskii and Aleksandr A. Ershov},
  journal={2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA)},
  year={2017},
  pages={1-4}
}
We consider α set as a generalization of convex sets. In this paper it is proved that the distance from α-set to its convex hull in the Hausdorff metric is small. An estimate of this distance depending on the value of α.