Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Invariant measures in groups which are not locally compact


Author: John C. Oxtoby
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
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] P. Alexandroff and P. Urysohn, Über nulldimensionale Punktmengen, Math. Ann. vol.98 (1927) pp. 89-106.
  • [2] S. Banach, On Haar's measure, in S. Saks, Theory of the integral, Warsaw and Lwów, 1937, pp. 314-319.
  • [3] -, Théorie des opérations linéaires, Warsaw, 1932.
  • [4] C. Carathéodory, Vorlesungen über reellen Funktionen, Leipzig and Berlin, 1918.
  • [5] -, Über das lineare Mass von Punktmengen--eine Verallgemeinerung des Längenbegriffs, Nachr. Ges. Wiss. Göttingen, 1914, pp. 404-426.
  • [6] D. van Dantzig, Zur topologischen Algebra I, Math. Ann. vol. 107 (1933) pp. 587-626. MR 1512818
  • [7] A. Haar, Der Massbegriff in der Theorie der kontinuierlichen Gruppen, Ann. of Math. (2) vol. 34 (1933) pp. 147-169. MR 1503103
  • [8] P. R. Halmos, Comment on the real line, Bull. Amer. Math. Soc. vol. SO (1944) pp. 877-878. MR 0011301 (6:145e)
  • [9] G. Hamel, Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: $ f(x + y) = f(x) + f(y)$, Math. Ann. vol. 60 (1905) pp. 459-462. MR 1511317
  • [10] F. Hausdorff, Dimension und äusseres Mass, Math. Ann. vol. 79 (1919) pp. 157-179.
  • [11] -, Mengenlehre, 3rd ed., Berlin, 1935.
  • [12] S. Kakutani, Über die Metrisation der topologischen Gruppen, Proc. Imp. Acad. Tokyo vol. 12 (1936) pp. 82-84. MR 1568424
  • [13] A. Kolmogoroff, Beiträge zur Masstheorie, Math. Ann. vol. 107 (1933) pp. 351-366. MR 1512805
  • [14] C. Kuratowski, Topologie, vol. 1, Warsaw and Lwów, 1933.
  • [15] L. H. Loomis, Abstract congruence and the uniqueness of Haar measure, Ann. of Math. (2) vol. 46 (1945) pp. 348-355. MR 0011713 (6:205a)
  • [16] D. Maharam, On measure in abstract sets, Trans. Amer. Math. Soc. vol. 51 (1942) pp. 413-433. MR 0006594 (4:11d)
  • [17] J. von Neumann, The uniqueness of Haar's measure, Rec. Math. (Mat. Sbornik) N.S. vol. 1 (1936) pp. 721-734.
  • [18] J. C. Oxtoby, Note on transitive transformations Proc. Nat. Acad. Sci. U.S.A. vol. 23 (1937) pp. 443-446.
  • [19] J. C. Oxtoby and S. M. Ulam, On the existence of a measure invariant under a transformation, Ann. of Math. (2) vol. 40 (1939) pp. 560-566. MR 0000097 (1:18e)
  • [20] L. Pontrjagin, Topological groups, Princeton, 1939.
  • [21] -, The theory of topological commutative groups, Ann. of Math. (2) vol. 35 (1934) pp. 361-388. MR 1503168
  • [22] J. Schreier and S. Ulam, Über topologische Abbildungen der euklidischen Sphären, Fund. Math. vol. 23 (1934) pp. 102-118.
  • [23] -, Über die Permutationsgruppe der natürlichen Zahlenfolge, Studia Mathematica vol. 4 (1933) pp. 134-141.
  • [24] A. Weil, L'intégration dans les groupes topologiques et ses applications, Actualités Scientifiques et Industrielles, no. 869, Paris, 1940.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20.0X

Retrieve articles in all journals with MSC: 20.0X


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1946-0018188-5
Article copyright: © Copyright 1946 American Mathematical Society

American Mathematical Society