Giulio Ascoli (20 January 1843,
Trieste
Trieste ( , ; sl, Trst ; german: Triest ) is a city and seaport in northeastern Italy. It is the capital city, and largest city, of the autonomous region of Friuli Venezia Giulia, one of two autonomous regions which are not subdivided into prov ...
– 12 July 1896,
Milan
Milan ( , , Lombard: ; it, Milano ) is a city in northern Italy, capital of Lombardy, and the second-most populous city proper in Italy after Rome. The city proper has a population of about 1.4 million, while its metropolitan city h ...
) was a
Jewish-Italian mathematician. He was a student of the
Scuola Normale di Pisa
The Scuola Normale Superiore in Pisa (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students.
It was founded in 1810 wi ...
, where he graduated in 1868.
In 1872 he became Professor of Algebra and Calculus of the
Politecnico di Milano
The Polytechnic University of Milan () is the largest technical university in Italy, with about 42,000 students.
The university offers undergraduate, graduate and higher education courses in engineering, architecture and design.
Founded in 18 ...
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.
[According to .] In 1889, Italian mathematician
Cesare Arzelà
Cesare Arzelà (6 March 1847 – 15 March 1912) was an Italian mathematician who taught at the University of Bologna and is recognized for his contributions in the theory of functions, particularly for his characterization of sequences of continu ...
generalized Ascoli's Theorem into the
Arzelà–Ascoli theorem
The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous functions defined on a closed and bounded interv ...
, a practical sequential compactness criterion of functions.
[See .]
See also
*
Measure (mathematics)
*
Oscillation (mathematics)
In mathematics, the oscillation of a function or a sequence is a number that quantifies how much that sequence or function varies between its extreme values as it approaches infinity or a point. As is the case with limits, there are several def ...
*
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 G� ...
Notes
Biographical references
* .
*(in
Italian
Italian(s) may refer to:
* Anything of, from, or related to the people of Italy over the centuries
** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance language
*** Regional Ita ...
). 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
Jean-Gaston Darboux FAS MIF FRS FRSE (14 August 1842 – 23 February 1917) was a French mathematician.
Life
According this birth certificate he was born in Nîmes in France on 14 August 1842, at 1 am. However, probably due to the midnigh ...
, Giulio Ascoli,
Henry John Stephen Smith,
Ulisse Dini
Ulisse Dini (14 November 1845 – 28 October 1918) was an Italian mathematician and politician, born in Pisa. He is known for his contribution to real analysis, partly collected in his book "''Fondamenti per la teorica delle funzioni di variabil ...
,
Vito Volterra
Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations, being one of the founders of functional analysis.
Biography
Born in An ...
,
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
Polytechnic University of Milan faculty
19th-century Italian Jews
{{Italy-mathematician-stub