Giulio Ascoli (20 January 1843,
Trieste
Trieste ( , ; ) is a city and seaport in northeastern Italy. It is the capital and largest city of the Regions of Italy#Autonomous regions with special statute, autonomous region of Friuli-Venezia Giulia, as well as of the Province of Trieste, ...
,
Austrian Empire
The Austrian Empire, officially known as the Empire of Austria, was a Multinational state, multinational European Great Powers, great power from 1804 to 1867, created by proclamation out of the Habsburg monarchy, realms of the Habsburgs. Duri ...
– 12 July 1896,
Milan
Milan ( , , ; ) is a city in northern Italy, regional capital of Lombardy, the largest city in Italy by urban area and the List of cities in Italy, second-most-populous city proper in Italy after Rome. The city proper has a population of nea ...
) was a
Jewish-Italian mathematician. He was a student of the
Scuola Normale di Pisa, where he graduated in 1868.
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
A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems ...
. For example, Ascoli introduced
equicontinuity in 1884, a topic regarded as one of the fundamental concepts in the theory of real functions.
[According to .] In 1889, Italian mathematician
Cesare Arzelà generalized Ascoli's Theorem into the
Arzelà–Ascoli theorem, a practical sequential compactness criterion of functions.
[See .]
See also
*
Measure (mathematics)
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events. These seemingly distinct concepts ha ...
*
Oscillation (mathematics)
*
Riemann Integral
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. It was presented to the faculty at the University of Gö ...
Notes
Biographical references
* .
*(in
Italian). Available from the website of the.
References
*.
*. "''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
Hermann Hankel (14 February 1839 – 29 August 1873) was a German mathematician. Having worked on mathematical analysis during his career, he is best known for introducing the Hankel transform and the Hankel matrix.
Biography
Hankel was born on ...
,
Gaston Darboux, Giulio Ascoli,
Henry John Stephen Smith,
Ulisse Dini,
Vito Volterra,
Paul David Gustav du Bois-Reymond and
Carl Gustav Axel Harnack.
External links
Biographyin Italian.
Ascoli, Julioin the
Jewish Encyclopedia.
By Their Fruits Ye Shall Know Them: Some Remarks on the Interaction of General Topology with Other Areas of Mathematicsby T. Koetsier, J. Van Mill, an article containing a history of Ascoli's work on the
Arzelà-Ascoli theorem.
1843 births
1896 deaths
19th-century Italian mathematicians
Mathematical analysts
Academic staff of the Polytechnic University of Milan
19th-century Italian Jews
{{Italy-mathematician-stub