Symmetric measures on Cartesian products
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- by Edwin Hewitt and Leonard J. Savage
- Trans. Amer. Math. Soc. 80 (1955), 470-501
- DOI: https://doi.org/10.1090/S0002-9947-1955-0076206-8
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References
- P. S. Alexandroff and H. Hopf, Topologie I. Die Grundlehren der mathematischen Wissenschaften, vol. XLV, Berlin, Springer, 1935.
Paul Alexandroff and Paul Urysohn, Mémoire sur les espaces topologiques compacts, Verhandelingen der Koninklijke Akademie van Wetenschappen te Amsterdam, Afdeeling Natuurkunde (Eerste Sectie) vol. XIV, no. 1, Amsterdam, 1929.
T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, Ergebnisse der Mathematik und ihrer Grenzgebiete, Berlin, 1934. (Reprint, New York, Chelsea, 1948.)
- N. Bourbaki, Eléments de mathématique. XV. Première partie: Les structures fondamentales de l’analyse. Livre V: Espaces vectoriels topologiques. Chapitre I: Espaces vectoriels topologiques sur un corps valué. Chapitre II: Ensembles convexes et espaces localement convexes, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1189, Hermann & Cie, Paris, 1953 (French). MR 0054161 —, Éléments de mathématique. First part, Book VI, Intégration, Chapters I-IV, Actualités Scientifiques et Industrielles, no. 1175, Paris, Hermann, 1952. Harald Cramér, Mathematical methods of statistics, Princeton University Press, 1951.
- J. L. Doob, Application of the theory of martingales, Le Calcul des Probabilités et ses Applications., Colloques Internationaux du Centre National de la Recherche Scientifique, no. 13, Centre National de la Recherche Scientifique, Paris, 1949, pp. 23–27 (French). MR 0033460
- J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896
- E. B. Dynkin, Classes of equivalent random quantities, Uspehi Matem. Nauk (N.S.) 8 (1953), no. 2(54), 125–130 (Russian). MR 0055601 Bruno de Finetti, Funzione caratteristica di un fenomeno aleatorio, Atti della R. Accademia Nazionale dei Lincei, Ser. 6, Memorie, Classe di Scienze Fisiche, Matematiche e Naturali vol. 4 (1931) pp. 251-299.
- Bruno de Finetti, La prévision : ses lois logiques, ses sources subjectives, Ann. Inst. H. Poincaré 7 (1937), no. 1, 1–68 (French). MR 1508036 Maurice Fréchet, Les probabilités associées à un système d’événements compatibles et dépendants. II, Actualités Scientifiques et Industrielles, no. 942, Paris, Hermann, 1943. Jules Haag, Sur un problème général de probabilités et ses diverses applications, Proceedings of the International Congress of Mathematicians, Toronto, 1924, Toronto, 1928, pp. 659-674.
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
- Felix Hausdorff, Grundzüge der Mengenlehre, Chelsea Publishing Co., New York, N. Y., 1949 (German). MR 0031025
- Edwin Hewitt, Linear functionals on spaces of continuous functions, Fund. Math. 37 (1950), 161–189. MR 42684, DOI 10.4064/fm-37-1-161-189 Edwin Hewitt and L. J. Savage, Bull. Amer. Math. Soc. Abstract 59-4-523. A. Ya. Hinčin, O klassah ekvivalentnyh sobytiǐ, Doklady Akad. Nauk SSSR vol. 85 (1952) pp. 713-714. —, Sur les classes d’événements équivalents, Mat. Sbornik vol. 39 (1932) pp. 40-43.
- M. Krein and D. Milman, On extreme points of regular convex sets, Studia Math. 9 (1940), 133–138 (English, with Ukrainian summary). MR 4990, DOI 10.4064/sm-9-1-133-138
- L. H. Loomis, On the representation of $\sigma$-complete Boolean algebras, Bull. Amer. Math. Soc. 53 (1947), 757–760. MR 0021084, DOI 10.1090/S0002-9904-1947-08866-2
- John C. Oxtoby, Ergodic sets, Bull. Amer. Math. Soc. 58 (1952), 116–136. MR 47262, DOI 10.1090/S0002-9904-1952-09580-X
- B. J. Pettis, On integration in vector spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 277–304. MR 1501970, DOI 10.1090/S0002-9947-1938-1501970-8
- Leonard J. Savage, The foundations of statistics, John Wiley & Sons, Inc., New York; Chapman & Hill, Ltd., London, 1954. MR 0063582
- M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375–481. MR 1501905, DOI 10.1090/S0002-9947-1937-1501905-7
- M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), no. 1, 37–111. MR 1501865, DOI 10.1090/S0002-9947-1936-1501865-8
- Minoru Tomita, On the regularly convex hull of a set in a conjugate Banach space, Math. J. Okayama Univ. 3 (1954), 143–145. MR 61770
- Kôsaku Yosida and Edwin Hewitt, Finitely additive measures, Trans. Amer. Math. Soc. 72 (1952), 46–66. MR 45194, DOI 10.1090/S0002-9947-1952-0045194-X
Bibliographic Information
- © Copyright 1955 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 80 (1955), 470-501
- MSC: Primary 60.0X
- DOI: https://doi.org/10.1090/S0002-9947-1955-0076206-8
- MathSciNet review: 0076206