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Keywords:
Kurzweil integral; regulated functions
Kurzweil integral; regulated functions
Summary:
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.
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