Giuseppe Vitali

Giuseppe Vitali
Born	26 August 1875(1875-08-26) Ravenna, Italy
Died	29 February 1932(1932-02-29) (aged 56) Bologna, Italy
Nationality	Italian
Fields	Mathematics

Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis.

Mathematical contributions

Vitali was the first to give an example of a non-measurable subset of real numbers, see Vitali set. His covering theorem is a fundamental result in measure theory. He also proved several theorems concerning convergence of sequences of measurable and holomorphic functions. Vitali convergence theorem generalizes Lebesgue's dominated convergence theorem. Another theorem bearing his name gives a sufficient condition for the uniform convergence of a sequence of holomorphic functions on an open domain D⊂ℂ to a holomorphic function on D. This result has been generalized to normal families of meromorphic functions, holomorphic functions of several complex variables, and so on.

See also

• Vitali convergence theorem
• Vitali covering theorem
• Vitali-Hahn-Saks theorem
• Vitali set

Bibliography

• Tonolo, Angelo (1932), "Commemorazione di Giuseppe Vitali (Commemoration of Giuseppe Vitali)", Rendiconti del Seminario Matematico della Università di Padova 3: 67–81, JFM 58.0049.10, http://www.numdam.org/item?id=RSMUP_1932__3__67_0 , (in Italian). Available at Numdam.
• Tricomi, G. F. (1962), Giuseppe Vitali, "Matematici italiani del primo secolo dello stato unitario (Italian mathematicians of the first century of the unitary state)", Memorie dell'Accademia delle Scienze di Torino. Classe di Scienze fisiche matematiche e naturali, series IV I: 120, Zbl 0132.24405, http://www.dm.unito.it/sism/m_italiani/biografie/tricomi/vitali.html  (in Italian). Available from the website of the Società Italiana di Storia delle Matematiche.

References

• Vitali, Giuseppe (1908) [17 dicembre 1907], "Sui gruppi di punti e sulle funzioni di variabili reali (On groups of points and functions of real variables)", Atti dell'Accademia delle Scienze di Torino 43: 75–92, JFM 39.0101.05, archived from the original on 2009-03-31, http://www.archive.org/stream/attidellarealeac43real#page/228/mode/2up , (in Italian). The paper containing the first proof of Vitali covering theorem.

External links

• O'Connor, John J.; Robertson, Edmund F., "Giuseppe Vitali", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Vitali.html .