**Borel** created the first effective theory of the measure of sets of points beginning of the modern theory of functions of a real variable. He was also a co-author of the Heine-Borel Theorem.

- Honoré Borel was an intelligent man and for the first years of his son's life he educated him at home.
- Family friends urged Borel to enter the École Polytechnique, which was considered the more prestigious establishment, but he had other ideas.
- Borel was advised that a degree from the École Polytechnique would give him the best opportunities for a job in industry or business.
- the theory of measure, Borel's theory of divergent series, his theory of non-analytic continuation and the theory of quasi-analytic functions all derive from ideas which make their first appearance in this paper.
- And it contained the explicit statement and proof of the famous covering theorem which, quite inappropriately, acquired the name of the Heine-Borel theorem ...
- Later Borel spoke about the mathematicians who had influenced him most in his early years mentioning, among others, Camille Jordan, Émile Picard, Paul Appell, Édouard Goursat, Paul Painlevé and Marcel Brillouin.
- At almost exactly the same time that he was receiving his doctorate, when still only 22 years of age, Borel was appointed Maître de Conférence at the University of Lille.
- Borel achieved much over the next years, both in his career and in the outstanding mathematics which he produced.
- Marguerite Borel was an outstanding author, writing under the pen name Camille Marbo (Marbo being the first three letters of Marguerite and the first two of Borel), and received the distinction of being awarded the Prix Femina in 1913 for La Statue voilée Ⓣ(The veiled statue).
- In 1909 Borel was appointed to a chair of Theory of Functions created specially for him at the Sorbonne and he went on to hold this professorship until 1941.
- On the fall of Painléve in 1917, Borel returned for a time to the front ...
- Borel created the first effective theory of the measure of sets of points.
- Borel, although not the first to define the sum of a divergent series, was the first to develop a systematic theory for a divergent series which he did in 1899.
- In addition, between 1921 and 1927, Borel published a series of papers on game theory and became the first to define games of strategy.
- After 1924, Borel became active in the French government serving in the French Chamber of Deputies (1924-36) and as Minister of the Navy (1925-40).
- In 1946, when he was 75 years old, Borel published the fascinating book Les paradoxes de l'infini Ⓣ(The paradoxes of infinity).

Born 7 January 1871, Saint Affrique, Aveyron, Midi-Pyrénées, France. Died 3 February 1956, Paris, France.

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Analysis, Number Theory, Set Theory, Special Numbers And Numerals

Theorems: 1

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive