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 (MSC 2000): 26A39
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