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math.CA2012
Knot points of typical continuous functions
David Preiss, Shingo Saito
It is well known that most continuous functions are nowhere differentiable. Furthermore, in terms of Dini derivatives, most continuous functions are nondifferentiable in the strong…
math.CA2008
Continuity Points of Typical Bounded Functions
Shingo Saito
Kostyrko and Salat showed that if a linear space of bounded functions has an element that is discontinuous almost everywhere, then a typical element in the space is discontinuous a…