Marstrand's density theorem for arbitrary norms in the plane

Giacomo Del Nin; Andrea Merlo

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arXiv · 2508.15400

Marstrand's density theorem for arbitrary norms in the plane

Giacomo Del Nin·Andrea Merlo

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Abstract

We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite $\alpha$-dimensional density with respect to some norm, then $\alpha$ must be an integer.

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Giacomo Del Nin, Andrea Merlo. 2025-08-21. Marstrand's density theorem for arbitrary norms in the plane. https://arxiv.org/abs/2508.15400

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