  We prove the existence of the curvature measures for a class of $\cal U_{\rm
WDC}$ sets, which is a direct generalization of $\cal U_{\rm PR}$ sets studied
by Rataj and Z\"ahle. Moreover, we provide a simple characterisation of $\cal
U_{\rm WDC}$ sets in $\mathbb R^2$ and prove that in $\mathbb R^2$ the class of
$\cal U_{\rm WDC}$ sets contains essentially all classes of sets known to admit
curvature measures.

Metric Geometry