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  1. On the Convergence of Fourier Series of Computable Lebesgue Integrable Functions.Philippe Moser - 2010 - Mathematical Logic Quarterly 56 (5):461-469.
    This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of Lp-computable functions with a size notion, by introducing Lp-computable Baire categories. We show that Lp-computable Baire categories satisfy the following three basic properties. Singleton sets {f } are meager, suitable infinite unions of meager sets are meager, and the whole space of Lp-computable functions is not meager. We give an alternative characterization of meager sets via Banach-Mazur games. We (...)
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