Giuseppe Vitali ( born August 26, 1875 in Ravenna, † February 29, 1932 in Bologna ) was an Italian mathematician. He was known by the proof of the existence of sets, the Lebesgue measure are not ( Vitali sets ).
Giuseppe Vitali ended 1899, the study of mathematics at the Scuola Normale Superiore in Pisa. In the following two years he was assistant to Ulisse Dini. Due to financial problems then he worked as a teacher in Genoa and was active in the Socialist Party until it was disbanded by the fascists in 1922. Then he applied for professorships and was appointed first in Modena, then in Padua, and finally in 1930 in Bologna.
His main achievements consist in the introduction of the concept of absolute continuity and in the field of orthogonal systems of functions. Also Vitali has constructed the first non- Lebesgue measurable set. A named after Vitali theorem deals with holomorphic function sequences, see also theorem of Vitali.