Preprint
Inserted: 23 dec 2025
Last Updated: 23 dec 2025
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 simple applications, we obtain a rectifiability criterion for signed Radon measures and the extension of a result, due to Mattila, on measures having unique blow-up almost everywhere.
Keywords: Rectifiability, Tangent measures, unique blow-up
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