Corpus ID: 221995963

# On rectifiable measures in Carnot groups: structure theory

@article{Antonelli2020OnRM,
title={On rectifiable measures in Carnot groups: structure theory},
author={Gioacchino Antonelli and Andrea Merlo},
journal={arXiv: Metric Geometry},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: Metric Geometry
In this paper we prove the one-dimensional Preiss' theorem in the first Heisenberg group $\mathbb H^1$. More precisely we show that a Radon measure $\phi$ on $\mathbb H^1$ with positive and finite one-density with respect to the Koranyi distance is supported on a one-rectifiable set in the sense of Federer, i.e., it is supported on the countable union of the images of Lipschitz maps $A\subseteq \mathbb R\to\mathbb H^1$. The previous theorem is a consequence of a Marstrand-Mattila type… Expand
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