Analytic Sets history

Analytic sets definition appeared in N.N. Luzin memoir. The definition became the main point of accusations brought against Luzin by his disciples. In their opinion, another analytic sets definition has priority, crystallized in the famous formulation: “The A-operation, as well as A-sets, were named by Suslin in honor of P.S. Alexandrov, who discovered them.” Alexandrov’s influence opinion on A-sets discovery is popular to this day and thus explicitly or indirectly supports a number of accusations against Luzin. Analyzing Luzin’s memoir Russian translation 1953, we will show the internal contradictions of the alternative history and propose to return to the analytic sets history in its original version, presented in [2], [3], [4], [5]. References
[1] N.N. Luzin, Lekcii ob analiticheskih mnozhestvah i ih prilozheniyah (Lectures on Analytic Sets and Their Applications). Moscow, 1953. In original: L u s i n N. Leçons sur les ensembles analytiques et leurs applications.– Paris: Gauthier-Villars, 1930.
[2] N.N. Luzin, Sobranie Sochinenij (Collected Works), v.2. Moscow, 1958. https://rusneb.ru/catalog/000199_000009_005624210/
[3] D. Menshov, M. Lavrentiev. Uspekhi teorii funkcij dejstvitel'nogo peremennogo v SSSR (Advances in the Theory of Functions of a Real Variable in the USSR). Matematicheskij sbornik.1928, v.35, supplementary issue, 21–39.
[4] W. Sierpiński, O teorii mnozhestv (On Set Theory). Izdatel'stvo Prosveshchenie, Moskva, 1966
[5] W. Sierpinski. Introduction in General Topology. The university of Toronto Press, Toronto 1934
[6] A.V. Ostrovsky, Borelevskie mnozhestva kak summy kanonicheskih elementov (Borel Sets as Sums of Canonical Elements). Doklady Akademii nauk, 2007, t. 413, № 2, s. 163–167. https://elibrary.ru/item.asp?id=9505916
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