Geodesic
Mutually singular functions and computation of the lengths of curves
Izvestiya. Mathematics , Tome 70 (2006) no. 4, pp. 693-716

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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. 
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     author = {A. A. Dovgoshey and O. Martio},
     title = {Mutually singular functions and computation of the lengths of curves},
     journal = {Izvestiya. Mathematics },
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_4_a2/}
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A. A. Dovgoshey; O. Martio. Mutually singular functions and computation of the lengths of curves. Izvestiya. Mathematics , Tome 70 (2006) no. 4, pp. 693-716. http://geodesic.mathdoc.fr/item/IM2_2006_70_4_a2/