Luzin quickly established a School of Mathematics at Moscow University and Menshov became one of his fist research students along with P S Aleksandrov, M Ya Suslin, and A Ya Khinchin . Menshov's first degree was awarded in 1916 for the thesis which he wrote on The Riemann theory of trigonometric series which was examined by Egorov and Luzin . However, only three weeks after he graduated, Menshov discovered one of his most fundamental results on the uniqueness problem for trigonometric series.
Luzin mabilis na itinatag ng School of Mathematics sa Moscow University at Menshov ay naging isa sa kanyang mga kamao ng pananaliksik na mag-aaral kasama ang PS Aleksandrov, M Ya Suslin, at isang Ya Khinchin. Menshov ng unang degree ay iginawad sa 1916 para sa sanaysay na kung saan siya wrote on Riemann Ang teorya ng trigonometriko serye kung saan ay napagmasdan sa pamamagitan ng Egorov at Luzin. Gayunman, tanging ang tatlong linggo matapos siya ay nagtapos, Menshov natuklasan ng isa sa kanyang pinaka-pangunahing resulta sa uniqueness problema para sa trigonometriko serye.