Geodesic
A nonexistence result for the Kurzweil integral
Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 571-580

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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.
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.
DOI : 10.21136/MB.2002.133949
Classification : 26A39, 26A42
Keywords: Kurzweil integral; regulated functions 
Krejčí, Pavel; Kurzweil, Jaroslav. A nonexistence result for the Kurzweil integral. Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 571-580. doi: 10.21136/MB.2002.133949
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