We investigate several natural questions on the differentiability of certain strictly increasing singular functions. Furthermore, motivated by the observation that for each famous singular function f investigated in the past, f’(ξ) = 0 if f’(ξ) exists and is finite, we show how, for example, an increasing real function g can be constructed so that for all rational numbers x and g’(x) = 0 for almost all irrational numbers x.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-1-3,
author = {Gerald Kuba},
title = {On the differentiability of certain saltus functions},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {15-30},
zbl = {1251.26004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-1-3}
}
Gerald Kuba. On the differentiability of certain saltus functions. Colloquium Mathematicae, Tome 122 (2011) pp. 15-30. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm125-1-3/