Curvatures for unions of WDC sets

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