Published Paper

Inserted: 10 sep 2020
Last Updated: 8 dec 2025

Journal: Journal of Mathematical Analysis and Applications
Volume: 500
Number: 2
Pages: 20
Year: 2021
Doi: 10.1016/j.jmaa.2021.125120

Abstract:

A well known notion of $k$-rectifiable set can be formulated in any metric space using Lipschitz images of subsets of $\mathbb{R}^k$. We prove some characterizations of $k$-rectifiability, when the metric space is an arbitrary homogeneous group. In particular, we show that the a.e. existence of the $(k,\mathbb{G})$-approximate tangent group implies $k$-rectifiability.

Keywords: homogeneous group, approximate tangent group, rectifiability, Lipschitz mapping

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