Editing Weierstrass function (section)

==Density of nowhere-differentiable functions==

It turns out that the Weierstrass function is far from being an isolated example: although it is "pathological", it is also "typical" of continuous functions:
* In a [[Topology|topological]] sense: the set of nowhere-differentiable real-valued functions on [0,&nbsp;1] is [[comeager set|comeager]] in the [[vector space]] ''C''([0,&nbsp;1];&nbsp;'''R''') of all continuous real-valued functions on [0,&nbsp;1] with the topology of [[uniform convergence]].<ref>{{cite journal|author=Mazurkiewicz, S..|title=Sur les fonctions non-dérivables|journal=Studia Math.|issue=3|year=1931|volume=3|pages=92–94|doi=10.4064/sm-3-1-92-94|doi-access=free}}</ref><ref>{{cite journal|author=Banach, S.|title=Über die Baire'sche Kategorie gewisser Funktionenmengen|journal=Studia Math.|issue=3|year=1931|volume=3|pages=174–179|doi=10.4064/sm-3-1-174-179|doi-access=free}}</ref>
* In a [[Measure theory|measure-theoretic]] sense: when the space ''C''([0,&nbsp;1];&nbsp;'''R''') is equipped with [[classical Wiener measure]] ''γ'', the collection of functions that are differentiable at even a single point of [0,&nbsp;1] has ''γ''-[[measure zero]]. The same is true even if one takes finite-dimensional "slices" of ''C''([0,&nbsp;1];&nbsp;'''R'''), in the sense that the nowhere-differentiable functions form a [[prevalent and shy sets|prevalent subset]] of ''C''([0,&nbsp;1];&nbsp;'''R''').