A nonexistence result for the Kurzweil integral
Pavel Krejčí; Jaroslav Kurzweil
Mathematica Bohemica (2002)
- Volume: 127, Issue: 4, page 571-580
- ISSN: 0862-7959
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topKrejčí, Pavel, and Kurzweil, Jaroslav. "A nonexistence result for the Kurzweil integral." Mathematica Bohemica 127.4 (2002): 571-580. <http://eudml.org/doc/249016>.
@article{Krejčí2002,
abstract = {It is shown that there exist a continuous function $f$ and a regulated function $g$ defined on the interval $[0,1]$ such that $g$ vanishes everywhere except for a countable set, and the $K^*$-integral of $f$ with respect to $g$ does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.},
author = {Krejčí, Pavel, Kurzweil, Jaroslav},
journal = {Mathematica Bohemica},
keywords = {Kurzweil integral; regulated functions; Kurzweil integral; regulated functions; evolution variational inequalities},
language = {eng},
number = {4},
pages = {571-580},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A nonexistence result for the Kurzweil integral},
url = {http://eudml.org/doc/249016},
volume = {127},
year = {2002},
}
TY - JOUR
AU - Krejčí, Pavel
AU - Kurzweil, Jaroslav
TI - A nonexistence result for the Kurzweil integral
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 4
SP - 571
EP - 580
AB - It is shown that there exist a continuous function $f$ and a regulated function $g$ defined on the interval $[0,1]$ such that $g$ vanishes everywhere except for a countable set, and the $K^*$-integral of $f$ with respect to $g$ does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.
LA - eng
KW - Kurzweil integral; regulated functions; Kurzweil integral; regulated functions; evolution variational inequalities
UR - http://eudml.org/doc/249016
ER -
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