Curvatures for unions of WDC sets

Abstract

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

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