It is well known that most continuous functions are nowhere differentiable. Furthermore, in terms of Dini derivatives, most continuous functions are nondifferentiable in the strongest possible sense except in a small set of points. In this paper, we completely characterise families S of sets of points for which most continuous functions have the property that such small set of points belongs to S. The proof uses a topological zero-one law and the Banach-Mazur game.
|Number of pages||24|
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - 2014|
All Science Journal Classification (ASJC) codes
- Applied Mathematics