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Affine length and affine dimension of a 1-set of ℝ2

Published online by Cambridge University Press:  14 November 2011

Françoise Dibos
Françoise Dibos
Affiliation:
CEREMADE, Université Paris 9 Dauphine, Place de Lattre de Tassigny, 75775 Paris cedex 16, France email: dibos@ceremade.dauphine.fr
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Abstract

We propose here a way to extend to all the 1-set of ℝ2 the well-known affine length which was just defined for a C2 curve. Moreover, this leads us to define the affine dimension of a 1-set which can be used for discriminate rectifiable 1-sets from unrectifiable 1-sets of ℝ2.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 5 , 1996 , pp. 985 - 993
Copyright
Copyright © Royal Society of Edinburgh 1996

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