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Box dimension of the graph of a continuous function: a necessary condition. (English) Zbl 1187.28009

MSC:

28A78 Hausdorff and packing measures
28A80 Fractals
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References:

[1] Biacino, L.:Derivatives of fractional order of continuous functions, Ric. DiMat., 53 (2004), 231–254 · Zbl 1228.26011
[2] Biacino, L.: Hausdorff dimension of the diagram of -Holder continuous functions, Ric. Di Mat., 54 (2005), 229–243
[3] Falconer, K.J.: The Geometry of Fractal Sets. Cambridge University Press (1985) · Zbl 0587.28004
[4] Falconer, K.J.: Fractal Geometry: Mathematical Foundations and Applications. New York: John Wiley and Sons Ltd. (1990) · Zbl 0689.28003
[5] Mattila, P.: Geometry of Sets and Measures in Euclidean Spaces, Cambridge University Press (1995) · Zbl 0819.28004
[6] Kolwankar, K.M., Levy Vhel, J.: Measuring function smoothness with local fractional derivatives, Fract. Calc. Appl. An., 4 (2001), 285–301 · Zbl 1044.26003
[7] Tricot, C.: Two definitions of fractional dimension, Math. Proc. Cambridge Phil. Soc., 91 (1982), 57–94 · Zbl 0483.28010 · doi:10.1017/S0305004100059119
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