Real Analysis Exchange

Examples Illustrating the Instability of Packing Dimensions of Sections

K. J. Falconer, M. Järvenpää, and P. Mattila

Full-text: Open access

Abstract

We shall use the ``iterated Venetian blind'' construction to show that the packing dimensions of plane sections of subsets of $\mathbb R^n$ can depend essentially on the directions of the planes. We shall also establish the instability of the packing dimension of sections under smooth diffeomorphisms.

Article information

Source
Real Anal. Exchange, Volume 25, Number 2 (1999), 629-640.

Dates
First available in Project Euclid: 3 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230995397

Mathematical Reviews number (MathSciNet)
MR1778515

Zentralblatt MATH identifier
1016.28006

Subjects
Primary: 28A12: Contents, measures, outer measures, capacities 28A80: Fractals [See also 37Fxx]

Keywords
packing dimension plane sections iterated constructions

Citation

Falconer, K. J.; Järvenpää, M.; Mattila, P. Examples Illustrating the Instability of Packing Dimensions of Sections. Real Anal. Exchange 25 (1999), no. 2, 629--640. https://projecteuclid.org/euclid.rae/1230995397


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