On the differentiability of certain saltus functions

Gerald Kuba. "On the differentiability of certain saltus functions." Colloquium Mathematicae 125.1 (2011): 15-30. <http://eudml.org/doc/283687>.

@article{GeraldKuba2011,
abstract = {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 $g^\{\prime \}(x) = 2^\{x\}$ for all rational numbers x and g’(x) = 0 for almost all irrational numbers x.},
author = {Gerald Kuba},
journal = {Colloquium Mathematicae},
keywords = {singular function; vanishing derivative; infinite derivative},
language = {eng},
number = {1},
pages = {15-30},
title = {On the differentiability of certain saltus functions},
url = {http://eudml.org/doc/283687},
volume = {125},
year = {2011},
}

TY - JOUR
AU - Gerald Kuba
TI - On the differentiability of certain saltus functions
JO - Colloquium Mathematicae
PY - 2011
VL - 125
IS - 1
SP - 15
EP - 30
AB - 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 $g^{\prime }(x) = 2^{x}$ for all rational numbers x and g’(x) = 0 for almost all irrational numbers x.
LA - eng
KW - singular function; vanishing derivative; infinite derivative
UR - http://eudml.org/doc/283687
ER -