## The Uniqueness Problem of the Representation of Functions by Trigonometric Series |

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algebraic integers algebraic numbers arbitrarily small arbitrary bounded variation Cantor consider constant ratio constructed contiguous interval continuous function converges to zero D. E. Men'sov definition denote denumerable deviation zero equal to zero exist field K(6 finite number fm(x following theorem formula 7.2 Fourier series Fourier-Stieltjes coefficients function F(x Georg Cantor given set H-set Hence homothetic transformation inequality interval contiguous interval of length intervals removed lemma M-set Math meas measure zero modulo monotone monotone functions N. K. Bari Pisot number positive integer problem proof prove reduced kernel remaining segments restricted sense segments of length series are zero set of measure set of points set of type set situated sets of constant sets with variable Sreider symmetric perfect sets symmetric set terval Theory of functions tion trigono trigonometric integrals type H U-set University of Moscow Verblunsky W-set W-set for trigonometric Zygmund