Abstract
We study WDC sets, which form a substantial generalization of sets with positive reach and still admit the definition of curvature measures. Main results concern WDC sets A subset of R-2.
We prove that, for such A, the distance function d(A) = dist(., A) is a "DC aura" for A, which implies that each closed locally WDC set in R-2 is a WDC set. Another consequence is that compact WDC subsets of R-2 form a Borel subset of the space of all compact sets.