Men'shov example of a zero-series

The first non-trivial example of a trigonometric series that converges to zero in the complement of a perfect set of measure zero; constructed by D.E. Men'shov [1]. A series with this property is called a zero-series. A problem naturally connected with this notion is that of the uniqueness of a trigonometric series of a function (see Uniqueness set).

References

[1]	D.E. Men'shov, "Sur l'unicité du développement trigonométrique" C.R. Acad. Sci. Paris , 163 (1916) pp. 433–436
[2]	N.K. [N.K. Bari] Bary, "A treatise on trigonometric series" , Pergamon (1964) (Translated from Russian)

References

[a1]	A. Zygmund, "Trigonometric series" , 1–2 , Cambridge Univ. Press (1988)