Submitted Paper
Inserted: 23 dec 2025
Last Updated: 16 apr 2026
Year: 2025
Abstract:
We show that the set of points where the blow-up, in the sense of Preiss, of a signed Radon measure on $\mathbb{R}^n$ is unique and its invariant subspace has dimension $k$ is $k$-rectifiable. As applications, we obtain simple proofs of a rectifiability criterion for Radon measures and of a theorem, due to Mattila, on measures having unique blow-up almost everywhere.
Keywords: Rectifiability, Tangent measures, unique blow-up
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