Hypersurfaces of the Heisenberg Group Are N-rectifiable
نویسنده
چکیده
Definition 1. Let N ′ be a Carnot group and N be a subgroup of N ′ with Hausdorff dimension k. A subset E of another Carnot Group (M,dM ) is said to be N -rectifiable if there exists U , a positive measure subset of N , and a Lipschitz map f : U → M such that H k M (E \ f(U)) = 0. We say E is countably N -rectifiable if there exist a countable number of pairs of subsets Ui and Lipschitz maps fi : Ui →M with H k M (E \ ∪ifi(Ui)) = 0.
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ar X iv : m at h / 04 07 22 3 v 1 [ m at h . D G ] 1 3 Ju l 2 00 4 C 1 HYPERSURFACES OF THE HEISENBERG GROUP ARE N - RECTIFIABLE
Definition 1. Let N ′ be a Carnot group and N be a subgroup of N ′ with Hausdorff dimension k. A subset E of another Carnot Group (M,dM ) is said to be N -rectifiable if there exists U , a positive measure subset of N , and a Lipschitz map f : U → M such that H k M (E \ f(U)) = 0. We say E is countably N -rectifiable if there exist a countable number of pairs of subsets Ui and Lipschitz maps fi...
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