Abstract
Most functions from the unit interval to itself have a graph with Hausdorff and lower entropy dimension 1 and upper entropy dimension 2. The same holds for several other Baire spaces of functions. In this paper it will be proved that this is the case also in the spaces of all mappings that are Lebesgue measurable, Borel measurable, integrable in the Riemann sense, continuous, uniform distribution preserving (and continuous).
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Schmeling, J., Winkler, R. Typical dimension of the graph of certain functions. Monatshefte für Mathematik 119, 303–320 (1995). https://doi.org/10.1007/BF01293590
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DOI: https://doi.org/10.1007/BF01293590