Besicovitch Functions

  • Marek Jarnicki
  • Peter Pflug
Part of the Springer Monographs in Mathematics book series (SMM)


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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marek Jarnicki
    • 1
  • Peter Pflug
    • 2
  1. 1.Institute of MathematicsJagiellonian UniversityKrakówPoland
  2. 2.Insitute for MathematicsCarl von Ossietzky University OldenburgOldenburgGermany

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