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typical function; box dimension; one-to-one function

References:

[1] S. J. Agronsky, A. M. Bruckner, M. Laczkovich: **Dynamics of typical continuous functions**. J. London Math. Soc. 40 (1989), 227–243. MR 1044271

[2] M. Elekes, T. Keleti: **Borel sets which are null or non-sigma-finite for every translation invariant measure**. Adv. Math. 201 (2006), 102–115. DOI 10.1016/j.aim.2004.11.009 | MR 2204751

[3] K. J. Falconer: **The geometry of fractal sets**. Cambridge Tracts in Mathematics, vol. 85, 1985. MR 0867284 | Zbl 0587.28004

[4] K. J. Falconer: **Fractal Geometry: Mathematical Foundations and Applications**. John Wiley & Sons, 1990. MR 1102677 | Zbl 0689.28003

[5] P. Mattila: **Geometry of Sets and Measures in Euclidean Spaces**. Cambridge University Press, 1995. MR 1333890 | Zbl 0819.28004