Abstract

It is proven that, if the Riemann sums of a trigonometric series are bounded everywhere, perhaps, except for some countable set and converge in measure to a bounded function \(f\), then this series is the Fourier series of the function \(f\). This implies the generalizations of the Cantor and Young theorems.

中文翻译：

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三角级数的唯一性

摘要

证明了，如果一个三角级数的黎曼和总有界，也许除了有一些可数集并在一定程度上收敛到有界函数\（f \），那么这个级数就是函数\（的傅立叶级数f \）。这意味着Cantor和Young定理的推广。