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Izvestiya: Mathematics, 2006, Volume 70, Issue 4, Pages 693–716
DOI: https://doi.org/10.1070/IM2006v070n04ABEH002324 (Mi im715) 		 
Mutually singular functions and computation of the lengths of curves

A. A. Dovgosheya, O. Martiob

a Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
b University of Helsinki, Department of Mathematics and Statistics
English version PDF (406 kB) Russian version article
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DOI: https://doi.org/10.1070/IM2006v070n04ABEH002324
Abstract: We study rectifiable curves given by mutually singular coordinate functions in finite-dimensional normed spaces. We describe these curves in terms of the behaviour of approximative tangents and find a simple formula for their lengths. We deduce from these results new necessary and sufficient conditions for the mutual singularity of finitely many functions of bounded variation.
Received: 11.05.2005
Bibliographic databases:
UDC: 517.52+517.98
MSC: 26B15, 28A75
Language: English
Original paper language: Russian
Citation: A. A. Dovgoshey, O. Martio, “Mutually singular functions and computation of the lengths of curves”, Izv. Math., 70:4 (2006), 693–716
Citation in format AMSBIB
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\by A.~A.~Dovgoshey, O.~Martio
\paper Mutually singular functions and computation of the lengths of curves
\jour Izv. Math.
\yr 2006
\vol 70
\issue 4
\pages 693--716
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:492
    Russian version PDF:275
    English version PDF:13
    References:55
    First page:2
     
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