En utilisant une idée de E. Bishop et K. de Leeuw on donne d’abord une démonstration très simplifiée du théorème de représentation intégrale dans les convexes compacts métrisables. Puis on revient sur quelques points du travail de E. Bishop et K. de Leeuw pour en préciser la portée. Enfin on pose quelques problèmes.
@article{AIF_1960__10__333_0, author = {Choquet, Gustave}, title = {Le th\'eor\`eme de repr\'esentation int\'egrale dans les ensembles convexes compacts}, journal = {Annales de l'Institut Fourier}, pages = {333--344}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {10}, year = {1960}, doi = {10.5802/aif.105}, mrnumber = {23 #A4003}, zbl = {0096.08201}, language = {fr}, url = {https://www.numdam.org/articles/10.5802/aif.105/} }
TY - JOUR AU - Choquet, Gustave TI - Le théorème de représentation intégrale dans les ensembles convexes compacts JO - Annales de l'Institut Fourier PY - 1960 SP - 333 EP - 344 VL - 10 PB - Institut Fourier PP - Grenoble UR - https://www.numdam.org/articles/10.5802/aif.105/ DO - 10.5802/aif.105 LA - fr ID - AIF_1960__10__333_0 ER -
%0 Journal Article %A Choquet, Gustave %T Le théorème de représentation intégrale dans les ensembles convexes compacts %J Annales de l'Institut Fourier %D 1960 %P 333-344 %V 10 %I Institut Fourier %C Grenoble %U https://www.numdam.org/articles/10.5802/aif.105/ %R 10.5802/aif.105 %G fr %F AIF_1960__10__333_0
Choquet, Gustave. Le théorème de représentation intégrale dans les ensembles convexes compacts. Annales de l'Institut Fourier, Tome 10 (1960), pp. 333-344. doi : 10.5802/aif.105. https://www.numdam.org/articles/10.5802/aif.105/
[1] Existence et unicité des représentations intégrales au moyen des points extrémaux dans les cônes convexes, Séminaire Bourbaki, décembre 1956. | Numdam | MR | Zbl
,[2] The representation of linear functionals by measures on sets of extreme points. Annales de l'Institut Fourier, Tome 9, 1959, p. 305-331. | Numdam | Zbl
et ,- A New Look on Korovkin Theorem, Mediterranean Journal of Mathematics, Volume 21 (2024) no. 8 | DOI:10.1007/s00009-024-02755-5
- A Lévy–Khinchin formula for the space of infinite dimensional square complex matrices, Bulletin des Sciences Mathématiques, Volume 139 (2015) no. 3, p. 283 | DOI:10.1016/j.bulsci.2014.09.002
- Majorization of invariant measures for orientation-reversing maps, Ergodic Theory and Dynamical Systems, Volume 30 (2010) no. 5, p. 1471 | DOI:10.1017/s0143385709000686
- Multifractal analysis for disintegrations of Gibbs measures and conditional Birkhoff averages, Ergodic Theory and Dynamical Systems, Volume 29 (2009) no. 3, p. 885 | DOI:10.1017/s0143385708000655
- Stock Prices and the Real Economy: Power Law versus Exponential Distributions, Journal of Economic Interaction and Coordination, Volume 1 (2006) no. 1, p. 45 | DOI:10.1007/s11403-006-0003-x
- Insensitive versus efficient dynamic load balancing in networks without blocking, Queueing Systems, Volume 54 (2006) no. 3, p. 193 | DOI:10.1007/s11134-006-0066-3
- Overdispersed and underdispersed Poisson generalizations, Journal of Statistical Planning and Inference, Volume 134 (2005) no. 2, p. 486 | DOI:10.1016/j.jspi.2004.04.019
- Are rich people smarter?, Journal of Economic Theory, Volume 110 (2003) no. 1, p. 42 | DOI:10.1016/s0022-0531(03)00024-3
- Investment Talent and the Pareto Wealth Distribution: Theoretical and Experimental Analysis, Review of Economics and Statistics, Volume 85 (2003) no. 3, p. 709 | DOI:10.1162/003465303322369830
- Infinite Dimensional Convexity, Volume 1 (2001), p. 599 | DOI:10.1016/s1874-5849(01)80017-6
- , Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569), Volume 1 (2001), p. 167 | DOI:10.1109/nafips.2001.944246
- Some geometric properties of the set of generalized Young functionals, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 129 (1999) no. 3, p. 601 | DOI:10.1017/s0308210500021521
- Linear stochastic dynamics with nonlinear fractal properties, Physica A: Statistical Mechanics and its Applications, Volume 250 (1998) no. 1-4, p. 295 | DOI:10.1016/s0378-4371(97)00543-8
- Potential at Infinity on Symmetric Spaces and Martin Boundary, Harmonic Analysis and Discrete Potential Theory (1992), p. 23 | DOI:10.1007/978-1-4899-2323-3_3
- On the boundary barycentric calculus, Journal of Functional Analysis, Volume 78 (1988) no. 1, p. 85 | DOI:10.1016/0022-1236(88)90133-4
- Bibliography, Probabilities and Potential C - Potential Theory for Discrete and Continuous Semigroups, Volume 151 (1988), p. 387 | DOI:10.1016/s0304-0208(08)71921-2
- The topological space of all extreme points of a compact convex set, Rendiconti del Circolo Matematico di Palermo, Volume 37 (1988) no. 2, p. 177 | DOI:10.1007/bf02844522
- An alternative approach to multiply self-decomposable probability measures on Banach spaces, Probability Theory and Related Fields, Volume 72 (1986) no. 1, p. 35 | DOI:10.1007/bf00343895
- A lattice-theoretic characterization of choquet simplexes, Operator Algebras and their Connections with Topology and Ergodic Theory, Volume 1132 (1985), p. 517 | DOI:10.1007/bfb0074907
- Optimal reinsurances, Scandinavian Actuarial Journal, Volume 1984 (1984) no. 2, p. 65 | DOI:10.1080/03461238.1984.10413754
- A note on Pólya’s theorem, Trabajos de Estadistica y de Investigacion Operativa, Volume 35 (1984) no. 1, p. 104 | DOI:10.1007/bf02888783
- “Sobre los modelos jerárquicos y su relación con el problema de decisión con información parcial a priori”, Trabajos de Estadistica y de Investigacion Operativa, Volume 35 (1984) no. 2, p. 222 | DOI:10.1007/bf02888903
- References, Convex Cones, Volume 56 (1981), p. 403 | DOI:10.1016/s0304-0208(08)71030-2
- References, Convexity Theory and its Applications in Functional Analysis (1980), p. 252 | DOI:10.1016/b978-0-12-065340-9.50011-5
- V-decomposable measures on hilbert spaces, Probability Theory on Vector Spaces II, Volume 828 (1980), p. 108 | DOI:10.1007/bfb0097398
- Decomposition Theory, Operator Algebras and Quantum Statistical Mechanics (1979), p. 309 | DOI:10.1007/978-3-662-02313-6_4
- Gleason Measures, Probabilistic Analysis and Related Topics (1979), p. 69 | DOI:10.1016/b978-0-12-095602-9.50007-4
- SELECTED BIBLIOGRAPHY, Measure and Integral (1978), p. 549 | DOI:10.1016/b978-0-12-378550-3.50023-2
- On a Class of Limit Laws, Theory of Probability Its Applications, Volume 23 (1978) no. 1, p. 206 | DOI:10.1137/1123024
- Convex sets, extreme points, and simplexes, Journal of Soviet Mathematics, Volume 4 (1975) no. 6, p. 625 | DOI:10.1007/bf01083882
- Extreme point method in probability theory, Probability-Winter School, Volume 472 (1975), p. 169 | DOI:10.1007/bfb0081953
- Martin-Dynkin boundaries of random fields, Communications in Mathematical Physics, Volume 36 (1974) no. 4, p. 321 | DOI:10.1007/bf01646203
- Un théorème d'unicité pour les hyperplans poissoniens, Journal of Applied Probability, Volume 11 (1974) no. 01, p. 184 | DOI:10.1017/s0021900200036536
- Un théorème d'unicité pour les hyperplans poissoniens, Journal of Applied Probability, Volume 11 (1974) no. 1, p. 184 | DOI:10.2307/3212596
- Extremalpunkte konvexer Mengen, Selecta Mathematica III, Volume 86 (1971), p. 90 | DOI:10.1007/978-3-642-65153-3_4
- Martin boundaries for the direct product of Markov processes, Siberian Mathematical Journal, Volume 11 (1970) no. 2, p. 280 | DOI:10.1007/bf00967302
- Lois ind�finiment divisibles sur l'espace des distributions, Inventiones Mathematicae, Volume 3 (1967) no. 4, p. 282 | DOI:10.1007/bf01402953
- Factorization of probability measures on locally compact groups, Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Volume 8 (1967) no. 3, p. 231 | DOI:10.1007/bf00531525
- An application of extreme point methods to the representation of infinitely divisible distributions, Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Volume 5 (1966) no. 4, p. 304 | DOI:10.1007/bf00535361
- Translation-invariant cones of functions on semi-simple lie groups, Bulletin of the American Mathematical Society, Volume 71 (1965) no. 2, p. 271 | DOI:10.1090/s0002-9904-1965-11283-6
- �ber unit�re Darstellungen abz�hlbarer, diskreter Gruppen, Mathematische Annalen, Volume 153 (1964) no. 2, p. 111 | DOI:10.1007/bf01361180
- The generation of convex hulls, Mathematische Annalen, Volume 152 (1963) no. 1, p. 1 | DOI:10.1007/bf01343728
- Extreme-point methods in stochastic analysis, Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Volume 1 (1963) no. 3, p. 295 | DOI:10.1007/bf00532503
Cité par 43 documents. Sources : Crossref