Talk:Riemann-Lebesgue lemma

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[edit] extension

I think you can apply the theorem to functions over the whole real line, not just intervals, provided they're still L¹ of course. The proof has an extra technical step, but this is a much more useful result. For example, see Reed and Simon (though they prove it quite differently, and they also prove that not only does the Fourier Transform of the L¹ function exist, but that it is ). Lavaka 18:13, 13 September 2006 (UTC)