## 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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