A nonexistence result for the Kurzweil integral
Pavel Krejčí, Jaroslav Kurzweil (2002)
Mathematica Bohemica
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It is shown that there exist a continuous function and a regulated function defined on the interval such that vanishes everywhere except for a countable set, and the -integral of with respect to does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.