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Fourier transforms and the Kurtzweil-Henstock Kurzweil-Henstock integral

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

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