Approximate differentiation: Jarník points
Fundamenta Mathematicae, Tome 140 (1991) no. 1, pp. 87-97
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We investigate Jarník's points for a real function f defined in ℝ, i.e. points x for which $ap_{y → x}|(f(y)-f(x))/(y-x)|=+∞$. In 1970, Berman has proved that the set $J_f$ of all Jarník's points for a path f of the one-dimensional Brownian motion is the whole ℝ almost surely. We give a simple explicit construction of a continuous function f with $J_f = $ ℝ. The main result of our paper says that for a typical continuous function f on [0,1] the set $J_f$ is c-dense in [0,1].
@article{10_4064_fm_140_1_87_97,
author = {Jan Mal\'y and Lud\v{e}k Zaj{\i}́\v{c}ek},
title = {Approximate differentiation: {Jarn{\'\i}k} points},
journal = {Fundamenta Mathematicae},
pages = {87--97},
publisher = {mathdoc},
volume = {140},
number = {1},
year = {1991},
doi = {10.4064/fm-140-1-87-97},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-140-1-87-97/}
}
TY - JOUR AU - Jan Malý AU - Luděk Zajı́ček TI - Approximate differentiation: Jarník points JO - Fundamenta Mathematicae PY - 1991 SP - 87 EP - 97 VL - 140 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm-140-1-87-97/ DO - 10.4064/fm-140-1-87-97 LA - en ID - 10_4064_fm_140_1_87_97 ER -
Jan Malý; Luděk Zajı́ček. Approximate differentiation: Jarník points. Fundamenta Mathematicae, Tome 140 (1991) no. 1, pp. 87-97. doi: 10.4064/fm-140-1-87-97
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