Inserted: 21 jul 2020
Last Updated: 21 jul 2020
Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Volume: 19(3) (2019)
Defining the $m$-th stratum of a closed subset of an $n$ dimensional Euclidean space to consist of those points, where it can be touched by a ball from at least $n-m$ linearly independent directions, we establish that the $m$-th stratum is second-order rectifiable of dimension $m$ and a Borel set. This was known for convex sets, but is new even for sets of positive reach. The result is based on a new criterion for second-order rectifiability.