Luzin, Nikolai Nikolaevich

Born Nov. 27 (Dec. 9), 1883, in Tomsk; died Feb. 28, 1950, in Moscow. Soviet mathematician. Academician of the Academy of Sciences of the USSR (1929; corresponding member, 1927). Professor at Moscow University from 1917.

Luzin’s principal studies dealt with the theory of functions of a real variable. His dissertation The Integral and the Trigonometric Series (1915) contains fundamental results that exerted a decisive influence on the further development of the metric theory of functions. Luzin was one of the founders of the descriptive theory of functions, in which a particularly important development was the discovery of projective sets. Luzin conjectured that a number of problems connected with projective sets, in particular their measurability, cannot be solved in the classical sense, and his predictions were confirmed in the 1970’s using the methods of mathematical logic.

Luzin obtained important results regarding the boundary properties of analytic functions and the unique determination of analytic functions from their boundary values. He devoted a series of works to mathematical analysis, differential equations, and differential geometry. He obtained a best possible result for the problem of deformation of surfaces on the main base. The studies of Luzin and his followers made a fundamental contribution to the development of the theory of functions of a real variable.

Luzin’s followers include D. E. Men’shov, A. Ia. Khinchin, P. S. Aleksandrov, M. Ia. Suslin, M. A. Lavrent’ev, L. A. Liusternik, N. K. Bari, A. N. Kolmogorov, L. G. Shnirel’man, P. S. Novikov, and L. V. Keldysh. Luzin was awarded the Order of the Red Banner of Labor.