Is it possible to define Fourier transforms on locally compact commutative groups using the Kurzweil-Henstock integral instead of the Lebesgue integral?

Do none of those articles answer your question?
– Harry GindiMar 22 '10 at 8:59

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The question is essentially, can you use the Haar measure with the K-H integral. My guess is that it is not possible. The whole beauty of the Lebesgue integral is that it can be defined with respect to an arbitrary measure.
– Harry GindiMar 22 '10 at 14:01

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It's remarkable how quickly this question went to the top of the results for that search (at least on my computer).
– Mark MeckesMar 22 '10 at 16:21

Most of the Tulone and Skvortsov stuff seems to be for zero-dimensional LC groups.
– Steve HuntsmanMar 29 '10 at 4:03