Invariant measures in groups which are not locally compact
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- by John C. Oxtoby
- Trans. Amer. Math. Soc. 60 (1946), 215-237
- DOI: https://doi.org/10.1090/S0002-9947-1946-0018188-5
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References
- P. Alexandroff and P. Urysohn, Ăśber nulldimensionale Punktmengen, Math. Ann. vol.98 (1927) pp. 89-106.
S. Banach, On Haar’s measure, in S. Saks, Theory of the integral, Warsaw and Lwów, 1937, pp. 314-319.
—, Théorie des opérations linéaires, Warsaw, 1932.
C. Carathéodory, Vorlesungen über reellen Funktionen, Leipzig and Berlin, 1918.
—, Über das lineare Mass von Punktmengen—eine Verallgemeinerung des Längenbegriffs, Nachr. Ges. Wiss. Göttingen, 1914, pp. 404-426.
- D. van Dantzig, Zur topologischen Algebra, Math. Ann. 107 (1933), no. 1, 587–626 (German). MR 1512818, DOI 10.1007/BF01448911
- Alfred Haar, Der Massbegriff in der Theorie der kontinuierlichen Gruppen, Ann. of Math. (2) 34 (1933), no. 1, 147–169 (German). MR 1503103, DOI 10.2307/1968346
- Paul R. Halmos, Comment on the real line, Bull. Amer. Math. Soc. 50 (1944), 877–878. MR 11301, DOI 10.1090/S0002-9904-1944-08255-4
- Georg Hamel, Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: $f(x+y)=f(x)+f(y)$, Math. Ann. 60 (1905), no. 3, 459–462 (German). MR 1511317, DOI 10.1007/BF01457624 F. Hausdorff, Dimension und äusseres Mass, Math. Ann. vol. 79 (1919) pp. 157-179. —, Mengenlehre, 3rd ed., Berlin, 1935.
- Shizuo Kakutani, Über die Metrisation der topologischen Gruppen, Proc. Imp. Acad. Tokyo 12 (1936), no. 4, 82–84 (German). MR 1568424
- A. Kolmogoroff, Beiträge zur Maßtheorie, Math. Ann. 107 (1933), no. 1, 351–366 (German). MR 1512805, DOI 10.1007/BF01448898 C. Kuratowski, Topologie, vol. 1, Warsaw and Lwów, 1933.
- Lynn H. Loomis, Abstract congruence and the uniqueness of Haar measure, Ann. of Math. (2) 46 (1945), 348–355. MR 11713, DOI 10.2307/1969028
- Dorothy Maharam, On measure in abstract sets, Trans. Amer. Math. Soc. 51 (1942), 413–433. MR 6594, DOI 10.1090/S0002-9947-1942-0006594-0 J. von Neumann, The uniqueness of Haar’s measure, Rec. Math. (Mat. Sbornik) N.S. vol. 1 (1936) pp. 721-734. J. C. Oxtoby, Note on transitive transformations Proc. Nat. Acad. Sci. U.S.A. vol. 23 (1937) pp. 443-446.
- J. C. Oxtoby and S. M. Ulam, On the existence of a measure invariant under a transformation, Ann. of Math. (2) 40 (1939), 560–566. MR 97, DOI 10.2307/1968940 L. Pontrjagin, Topological groups, Princeton, 1939.
- L. Pontrjagin, The theory of topological commutative groups, Ann. of Math. (2) 35 (1934), no. 2, 361–388. MR 1503168, DOI 10.2307/1968438 J. Schreier and S. Ulam, Über topologische Abbildungen der euklidischen Sphären, Fund. Math. vol. 23 (1934) pp. 102-118. —, Über die Permutationsgruppe der natürlichen Zahlenfolge, Studia Mathematica vol. 4 (1933) pp. 134-141. A. Weil, L’intégration dans les groupes topologiques et ses applications, Actualités Scientifiques et Industrielles, no. 869, Paris, 1940.
Bibliographic Information
- © Copyright 1946 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 60 (1946), 215-237
- MSC: Primary 20.0X
- DOI: https://doi.org/10.1090/S0002-9947-1946-0018188-5
- MathSciNet review: 0018188