Besicovitch Functions

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.