Jean Choquet (30 June 1917 – 7 March 2009) was a French mathematician noted for his contributions to functional analysis, potential theory, topology, and game theory. His work laid the foundations for what is now known as Choquet theory, encompassing concepts such as the Choquet integral, Choquet capacity, and the Choquet boundary.
Early life and education
Jean Choquet was born in Lons‑le‑Saunier, France. He entered the École Normale Supérieure in 1935, where he studied mathematics under leading French scholars of the period. He completed his doctoral dissertation, Étude des fonctions de plusieurs variables réelles, in 1941, receiving his doctorate from the University of Paris. His doctoral advisor was Maurice Fréchet.
Academic career
After obtaining his doctorate, Choquet joined the Centre National de la Recherche Scientifique (CNRS) as a researcher. In 1945 he was appointed professor of mathematics at the University of Paris (Sorbonne), a position he held until his retirement in 1985. He also held visiting professorships and gave lectures at institutions in the United States, Canada, and several European countries.
Research contributions
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Choquet theory: Choquet introduced the concept of representing points of a convex compact set as barycenters of probability measures supported on its extreme points. This representation theorem, now known as the Choquet theorem, is a central result in convex analysis and functional analysis.
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Choquet integral: He defined a nonlinear integral with respect to a capacity (a non‑additive set function). The Choquet integral has found applications in decision theory, economics, and fuzzy set theory.
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Potential theory and capacity: Choquet developed a systematic theory of capacities, extending classical potential theory. His work on Choquet capacities provided a framework for studying fine properties of functions and sets.
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Topology: He contributed to the theory of Choquet spaces (also called Baire spaces), which are topological spaces where the intersection of countably many dense open sets is dense.
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Game theory: In collaboration with other mathematicians, Choquet applied his analytical methods to cooperative game theory, particularly in the study of value and core concepts.
Honors and recognition
- Elected member of the French Academy of Sciences (1970).
- Awarded the Grand Cross of the Legion of Honour (1990).
- Recipient of the Prix de l’État (State Prize) for mathematics (1965).
- Honorary doctorate from the University of Liège (1978).
Selected publications
- J. Choquet, Theory of Capacities, Annales de l'Institut Fourier, 1953.
- J. Choquet, Lectures on Analysis, Hermann, Paris, 1969.
- J. Choquet, Topologie et Analyse Fonctionnelle, Gauthier‑Villars, 1974.
Legacy
Jean Choquet’s theoretical developments have had lasting influence across several mathematical disciplines and continue to be applied in areas such as economics, engineering, and computer science. The concepts bearing his name—Choquet integral, Choquet capacity, and Choquet theorem—remain standard tools in modern analysis and decision theory.
