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A nonexistence result for the Kurzweil integral. (English) Zbl 1005.26005

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.

MSC:

26A39 Denjoy and Perron integrals, other special integrals
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