MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 571-580 (2002)

A nonexistence result for the Kurzweil integral

Pavel Krejci, Jaroslav Kurzweil

Pavel Krejci, Jaroslav Kurzweil, Mathematical Institute, Academy of Sciences of the Czech Republic, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail: krejci@math.cas.cz, kurzweil@math.cas.cz

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.

Keywords: Kurzweil integral, regulated functions

Classification (MSC2000): 26A39

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