Real Analysis Exchange

Examples Illustrating the Instability of Packing Dimensions of Sections

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

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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

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

First available in Project Euclid: 3 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

packing dimension plane sections iterated constructions


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.

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