Marstrand's density theorem for arbitrary norms in the plane
Classical Analysis and ODEs
2025-08-22 v1 Metric Geometry
Abstract
We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite -dimensional density with respect to some norm, then must be an integer.
Keywords
Cite
@article{arxiv.2508.15400,
title = {Marstrand's density theorem for arbitrary norms in the plane},
author = {Giacomo Del Nin and Andrea Merlo},
journal= {arXiv preprint arXiv:2508.15400},
year = {2025}
}