Giulio Ascoli

Giulio Ascoli (1843 to 1896) was a Jewish Italian mathematician, born in Trieste when it belonged to the Austrian Empire and died in Milan. He studied at the Scuola Normale di Pisa and graduated in 1868. In 1872 he became professor of algebra and calculus at the Politecnico di Milano, and from 1879 he held a chair of mathematics at the Reale Istituto Tecnico Superiore in Milan, where a plaque in his memory was later affixed. He was also a corresponding member of the Istituto Lombardo. His work belongs to the theory of functions of a real variable and to Fourier series. In 1884 he introduced equicontinuity, a notion regarded as one of the fundamental concepts of real function theory, and in 1889 Cesare Arzela generalized his result into the Arzela-Ascoli theorem, a practical criterion for the sequential compactness of families of functions.