Carlo Severini
Carlo Severini (10 March 1872 – 11 May 1951) was an Italian mathematician: he was born in Arcevia (Province of Ancona) and died in Pesaro. Severini, independently from Dmitri Fyodorovich Egorov, proved and published earlier a proof of the theorem now known as Egorov's theorem. Biography. He graduated in Mathematics from the University of Bologna on November 30, 1897: the title of his "Laurea" thesis was ""Sulla rappresentazione analitica delle funzioni arbitrarie di variabili reali"". After obtaining his degree, he worked in Bologna as an assistant to the chair of Salvatore Pincherle until 1900. From 1900 to 1906 , he was a senior high school teacher, first teaching in the Institute of Technology of La Spezia and then in the lyceums of Foggia and of Turin; then, in 1906 he became full professor of Infinitesimal Calculus at the University of Catania. He worked in Catania until 1918, then he went to the University of Genova, where he stayed until his retirement in 1942. Work. He authored more than 60 papers, mainly in the areas of real analysis, approximation theory and partial differential equations, according to . His main contributions belong to the following fields of mathematics: Approximation theory. In this  field, Severini proved a generalized version of the Weierstrass approximation theorem. Precisely, he extended the original result of Karl Weierstrass to the class of bounded locally integrable functions, which is a class including particular discontinuous functions as members. Measure theory and integration. Severini proved Egorov's theorem one year earlier than Dmitri Egorov in the paper , whose main theme is however sequences of orthogonal functions and their properties. Partial differential equations. Severini proved an existence theorem for the Cauchy problem for the non linear hyperbolic partial differential equation of first order assuming that the Cauchy data formula_2 (defined in the  bounded interval formula_3) and that the function formula_4 has Lipschitz continuous first order partial derivatives, jointly with the obvious requirement that the set formula_5 is contained in the domain of formula_4. Real analysis and unfinished works. According to , he worked also on the foundations of the theory of real functions. Severini also left an unpublished and unfinished treatise on the theory of real functions, whose title was planned to be ""Fondamenti dell'analisi nel campo reale e i suoi sviluppi"".