Giulio Ascoli
Giulio Ascoli (20 January 1843, Trieste – 12 July 1896, Milan) was a JewishItalian[1] mathematician. He was a student of the Scuola Normale di Pisa, where he graduated in 1868.
Giulio Ascoli  

Born  Trieste, Italy  20 January 1843
Died  12 July 1896 53) Milan, Italy  (aged
Nationality  Italian 
Scientific career  
Fields  Mathematics 
In 1872 he became Professor of Algebra and Calculus of the Politecnico di Milano University. From 1879 he was professor of mathematics at the Reale Istituto Tecnico Superiore, where, in 1901, was affixed a plaque that remembers him.
He was also a corresponding member of Istituto Lombardo.
He made contributions to the theory of functions of a real variable and to Fourier series. For example, Ascoli introduced equicontinuity in 1884, a topic regarded as one of the fundamental concepts in the theory of real functions.[2] In 1889, Italian mathematician Cesare Arzelà generalized Ascoli's Theorem into the Arzelà–Ascoli theorem, a practical sequential compactness criterion of functions.[3]
Notes

This article incorporates text from a publication now in the public domain: Singer, Isidore; et al., eds. (1901–1906). "Ascoli, Giulio". The Jewish Encyclopedia. New York: Funk & Wagnalls.  According to Dshalalow (2000, p. 153).
 See Dshalalow (2000, p. 153).
Biographical references
 Guerraggio, Angelo; Nastasi, Pietro (2005), Italian mathematics between the two world wars, Science Networks. Historical Studies, 29, Basel: Birkhäuser Verlag, pp. x+299, doi:10.1007/3764375124, ISBN 3764365552, MR 2188015, Zbl 1084.01010.
 Tricomi, G. F. (1962). "Giulio Ascoli". 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. p. 120. Zbl 0132.24405. (in Italian). Available from the website of the Società Italiana di Storia delle Matematiche.
References
 Dshalalow, Jewgeni H. (2001), Real analysis: an introduction to the theory of real functions and integration, Studies in Advanced Mathematics, Boca Raton, Florida: CRC Press, pp. xiv+567, ISBN 1584880732, MR 1788725, Zbl 0978.28001.
 Letta, Giorgio (1994) [112°], "Le condizioni di Riemann per l'integrabilità e il loro influsso sulla nascita del concetto di misura" (PDF), Rendiconti della Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e applicazioni (in Italian), XVIII (1): 143–169, MR 1327463, Zbl 0852.28001, archived from the original (PDF) on 28 February 2014. "Riemann's conditions for integrability and their influence on the birth of the concept of measure" (English translation of title) is an article on the history of measure theory, analyzing deeply and comprehensively every early contribution to the field, starting from Riemann's work and going to the works of Hermann Hankel, Gaston Darboux, Giulio Ascoli, Henry John Stephen Smith, Ulisse Dini, Vito Volterra, Paul David Gustav du BoisReymond and Carl Gustav Axel Harnack.
External links
 Biography in Italian.
 Ascoli, Julio in the Jewish Encyclopedia.
 By Their Fruits Ye Shall Know Them: Some Remarks on the Interaction of General Topology with Other Areas of Mathematics by T. Koetsier, J. Van Mill, an article containing a history of Ascoli's work on the ArzelàAscoli theorem.