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The [[Fourier transform]] of an [[Lp space|''L''<sup>''1''</sup>]] function <math>f</math> on the [[real line]] <math>\mathbb R</math> is defined as the [[Lebesgue integral]]
<math display="block">\hat f(\xi) = \int_{\mathbb R} f(x)e^{-2\pi i x\xi}dx.</math>
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