### Abstract

In this article we calculate the exact location in the Borel hierarchy of UCF, the set of all continuous functions on the unit circle with uniformly convergent Fourier series. It turns out to be complete F_{σδ}. Also we prove that any G_{δσ} set that includes UCF must contain a continuous function with divergent Fourier series.

Original language | English |
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Pages (from-to) | 3507-3514 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 124 |

Issue number | 11 |

Publication status | Published - 1996 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics