# On measures in sub-Riemannian geometry

## TL;DR

This paper extends the analysis of measures in sub-Riemannian geometry by exploring Popp's measure and non-spherical Hausdorff measures, and discusses implications for metric measure spaces based on these manifolds.

## Contribution

It introduces new results on intrinsic measures in sub-Riemannian manifolds and examines their consequences for related metric measure spaces.

## Key findings

- Extended analysis to Popp's measure and non-spherical Hausdorff measures.
- Identified open questions and future research directions.
- Explored implications for metric measure spaces based on sub-Riemannian manifolds.

## Abstract

In \cite{gjha} we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim is to extend the study to other kinds of intrinsic measures on sub-Riemannian manifolds, namely Popp's measure and general (i.e., non spherical) Hausdorff measures. The second is to explore some consequences of \cite{gjha} on metric measure spaces based on sub-Riemannian manifolds.