On Differentiable Functions having an Everywhere Dense set of Intervals of Constancy
Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 73-76
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The Cantor function C [2; p. 213], which appears in analysis as a simple example of a continuous increasing function which is not absolutely continuous, has the following properties: (i) C is defined on [0,1], with C(0) = 0, C (l) = l; (ii) C is continuous and non-decreasing on [0,1]; (iii) C is constant on each interval contiguous to the perfect Cantor set P; (iv) C fails to be constant on any open interval containing points of P; (v) The set of points at which C is non-differentiable is non-denumerable.
Bruckner, A. M.; Leonard, John L. On Differentiable Functions having an Everywhere Dense set of Intervals of Constancy. Canadian mathematical bulletin, Tome 8 (1965) no. 1, pp. 73-76. doi: 10.4153/CMB-1965-009-1
@article{10_4153_CMB_1965_009_1,
author = {Bruckner, A. M. and Leonard, John L.},
title = {On {Differentiable} {Functions} having an {Everywhere} {Dense} set of {Intervals} of {Constancy}},
journal = {Canadian mathematical bulletin},
pages = {73--76},
year = {1965},
volume = {8},
number = {1},
doi = {10.4153/CMB-1965-009-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-009-1/}
}
TY - JOUR AU - Bruckner, A. M. AU - Leonard, John L. TI - On Differentiable Functions having an Everywhere Dense set of Intervals of Constancy JO - Canadian mathematical bulletin PY - 1965 SP - 73 EP - 76 VL - 8 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-009-1/ DO - 10.4153/CMB-1965-009-1 ID - 10_4153_CMB_1965_009_1 ER -
%0 Journal Article %A Bruckner, A. M. %A Leonard, John L. %T On Differentiable Functions having an Everywhere Dense set of Intervals of Constancy %J Canadian mathematical bulletin %D 1965 %P 73-76 %V 8 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1965-009-1/ %R 10.4153/CMB-1965-009-1 %F 10_4153_CMB_1965_009_1
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