Giuseppe Vitali

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Born in Ravenna, he studied in Pisa as Dini's pupil at the Scuola Normale Superiore. He continued to work in Pisa after graduating in 1899, as Dini's assistant. He immediately obtained important results in the theory of functions of one or more real variables. He interrupted his scientific activity when he left university to teach in middle school. He returned to research in 1923, at the University of Modena. He then moved to Padua and finally to Bologna in 1930 where he remained for two years, until his death. We owe him the concept of absolute continuity and the demonstration of the absolute continuity of the indefinite integral of an integrable function according to Lebesgue. He was also responsible for an important covering theorem which for many decades was used for issues of differentiation of functions of several real variables. He provided criteria for the analyticity of the limit of analytic functions, closure criteria of orthogonal systems and his "absolute differential calculus". Sansone completed and posthumously published the work "Moderna Teoria delle Funzioni di Variabili Reali" (Modern Theory of the Functions of Real Variables) (1935).

(Source: "Il Dipartimento di Matematica dell'Università di Bologna: Personale, strutture, attività di ricerca - Anno accademico 1988-89" a cura di M. Bernabei e P. Negrini, editrice CLUEB)