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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2009, Volume 6, Pages 522–525 (Mi semr82)  
Short communications

On the length of the set of extreme points for self-similar sets in $\mathbb R^2$

A. V. Tetenov

Gorno-Altaisk State University
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Abstract: We proof that the set of extreme points of the convex hull of any self-similar set in $\mathbb R^2$ has zero $1$-dimensional Lebesgue measure.
Keywords: self-similar sets, fractal, convex hull, extreme points, Hausdorff measure.
Received December 11, 2009, published December 12, 2009
Bibliographic databases:
Document Type: Article
UDC: 514.8, 515.12
MSC: 28A80
Language: English
Citation: A. V. Tetenov, “On the length of the set of extreme points for self-similar sets in $\mathbb R^2$”, Sib. Èlektron. Mat. Izv., 6 (2009), 522–525
Citation in format AMSBIB
\Bibitem{Tet09}
\by A.~V.~Tetenov
\paper On the length of the set of extreme points for self-similar sets in $\mathbb R^2$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2009
\vol 6
\pages 522--525
\mathnet{http://mi.mathnet.ru/semr82}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2586705}
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