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i have to show that the normal cycle of a convex subset is additive, i.e if A and B are two convex subsets then N(AUB)=N(A)+N(B)-N(A \inter B), i tought about using the Gauss-Bonnet formula since we it says that the total curvature equals the the euler caracteristic, and i have a relation between normal cycles and the curvature measures, so as the euler caracteristic is additive, i can get the result, but there's something missing since the additivity formula for normal cycle is only valid in the convex case, i don't know what's missing. Thanks for your help!

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