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

**Full text of the article:**

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