Summary
In Chap. 7, it was shown that \(\boldsymbol{\mathcal{B}}(\mathbb{I})\) is of first category in \(\mathcal{C}(\mathbb{I})\), i.e., most functions in \(\mathcal{C}(\mathbb{I})\) have somewhere on \(\mathbb{I}\) an infinite one-sided derivative. In the first part of this chapter, the construction of concrete functions belonging to \(\boldsymbol{\mathcal{B}}\boldsymbol{\mathcal{M}}(\mathbb{I})\) is discussed. The remaining part deals with a categorial argument proving that the set \(\boldsymbol{\mathcal{B}}\boldsymbol{\mathcal{M}}(\mathbb{I})\) is in some sense even a large set.
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Notes
- 1.
We thank Professor Jan Maly for the idea of the proof.
References
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Jarnicki, M., Pflug, P. (2015). Besicovitch Functions. In: Continuous Nowhere Differentiable Functions. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-12670-8_11
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DOI: https://doi.org/10.1007/978-3-319-12670-8_11
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