Summary
This chapter contains definitions and auxiliary results related to various notions of nowhere differentiability. In particular, in § 2.3, we present a proof of the famous Denjoy–Young–Saks theorem, which may permit the reader to understand better the sense of nowhere differentiability.
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Notes
- 1.
Recall that a pair (X, d) is a metric space if \(d: X \times X\longrightarrow \mathbb{R}_{+}\), (\(d(x,y) = 0\Longleftrightarrow x = y\)), d(x, y) = d(y, x), and d(x, y) ≤ d(x, z) + d(z, y). A set \(A \subset X\) is called open if for each a ∈ A, there exists an r > 0 such that \(\{x \in X: d(x,a) < r\} \subset A\).
References
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Jarnicki, M., Pflug, P. (2015). Preliminaries. In: Continuous Nowhere Differentiable Functions. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-12670-8_2
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