Abstract
Abstract We relate the Lipschitz–Killing measures of a definable set X ⊂ ℝ n in an o-minimal structure to the volumes of generic polar images. For smooth submanifolds of ℝ n , such results were established by Langevin and Shifrin. Then we give infinitesimal versions of these results. As a corollary, we obtain a relation between the polar invariants of Comte and Merle and the densities of generic polar images.
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