Marstrand type projection theorems for normed spaces

  • Zoltán M. Balogh

    Universität Bern, Switzerland
  • Annina Iseli

    Universität Bern, Switzerland, and University of California, Los Angeles, USA
Marstrand type projection theorems for normed spaces cover
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Abstract

We consider Marstrand type projection theorems for closest-point projections in the normed space . We prove that if a norm on is regular enough, then the analogues of the well-known statements from the Euclidean setting hold, while they fail for norms whose unit balls have corners. We establish our results by verifying Peres and Schlag’s transversality property and thereby also obtain a Besicovitch-Federer type characterization of purely unrectifiable sets.

Cite this article

Zoltán M. Balogh, Annina Iseli, Marstrand type projection theorems for normed spaces. J. Fractal Geom. 6 (2019), no. 4, pp. 367–392

DOI 10.4171/JFG/81