Ivan Privalov attended school in Novgorod, then entered the University of Moscow in 1909. He graduated in 1913 studying under Egorov and Luzin. His Master's Degree was awarded in 1916 and after this he taught at the University of Moscow.
In 1917 Privalov became professor at Saratov University where he remained for five years, then returned to Moscow. He was appointed professor of the theory of functions and complex variable there and he held this post for the rest of his life.
Privalov studied analytic functions in the vicinity of singular points by means of measure theory and Lebesgue integrals. He also obtained important results on conformal mappings showing that angles were preserved on the boundary almost everywhere.
Privalov wrote Cauchy Integral (1918) which built on work by Fatou. He also worked on many problems jointly with Luzin. In 1934 he studied subharmonic functions, building on the work of Riesz.
Article by: J J O'Connor and E F Robertson
December 1996