**Dmitrii Menshov** was a Russian mathematician known for his contributions to the theory of trigonometric series.

- In 1904, at the age of 12 years, Menshov began his secondary schooling.
- After leaving school, Menshov sat the entrance examination for the Moscow Engineering College and began his studies there in the autumn of 1911.
- Then in the autumn of 1912 Menshov entered the Department of Physics and Mathematics at Moscow University.
- Perhaps the most significant event for Menshov, however, was that Luzin returned from Göttingen to Moscow in the autumn of 1914 and began to lecture on functions of a real variable.
- Menshov attended Luzin's lecture course, and when Luzin posed the open problem of whether the Denjoy integral and the Borel integral were equivalent, he was able to solve the problem.
- The Denjoy integral is the more general of the two and Menshov showed that this was the case.
- Menshov's discovery, made while still an undergraduate, became his first publication.
- 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.
- By the end of 1918 Menshov had been awarded his Master's degree and he went to Ivanovo north-east of Moscow, which at that time was the temporary capital of the revolutionary government, but he soon moved to Nizhnii-Novgorod where he was appointed as a professor at the University.
- At this time Luzin and other members of his research school were in Ivanovo so Menshov was certainly in the mainstream of the exciting mathematics that was being developed.
- In the autumn of 1922 Menshov returned to Moscow and began teaching at the University.
- It may have been noticed by an attentive reader that we have still not noted that Menshov being awarded a doctorate (equivalent to the habilitation or D.Sc.).
- Together with the award of the doctorate came Menshov's appointment to a professorship at Moscow University.
- Privalov held this first chair up to 1941 but then, on Privalov's early death in that year, Menshov was appointed to the chair of the Theory of Functions.
- In 1943 these two chairs were combined and the Department of Theory of Functions and Functional Analysis was created with Menshov as its head.
- Menshov also worked a the Steklov Mathematical Institute of the USSR Academy of Sciences from 1934 to 1941 and then again from 1947.
- Menshov does not belong among the ranks of those mathematicians who undertake the solution of comparatively easy problems, or who continue the research of other authors on a course that has already been indicated.
- For his work on the representation of functions by trigonometric series, Menshov was awarded a State Prize in 1951.
- In 1958 Menshov attended the International Congress of Mathematicians in Edinburgh and he was invited to address the Congress with his paper On the convergence of trigonometric series.
- The first of the two pictures of Menshov which we have given was taken while he was at the Congress in Edinburgh, Scotland in 1958.

Born 18 April 1892, Moscow, Russia. Died 25 November 1988, Moscow, Russia.

View full biography at MacTutor

Origin Russia

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive