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)

 
 

 

Haar measure for measure groupoids


Author: Peter Hahn
Journal: Trans. Amer. Math. Soc. 242 (1978), 1-33
MSC: Primary 28C10; Secondary 22D40
DOI: https://doi.org/10.1090/S0002-9947-1978-0496796-6
MathSciNet review: 496796
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that Mackey's measure groupoids possess an analogue of Haar measure for locally compact groups; and many properties of the group Haar measure generalize. Existence of Haar measure for groupoids permits solution of a question raised by Ramsay. Ergodic groupoids with finite Haar measure are characterized.


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

  • [1] L. Auslander and C. C. Moore, Unitary representations of solvable Lie groups, Mem. Amer. Math. Soc. No. 62 (1966). MR 0207910 (34:7723)
  • [2] J. Dixmier, Algèbres quasi-unitaires, Comment. Math. Helv. 26 (1952), 275-322. MR 0052697 (14:660b)
  • [3] E. Effros, Global structure in von Neumann algebras, Trans. Amer. Math. Soc. 121 (1966), 434-454. MR 0192360 (33:585)
  • [4] J. Glimm, Families of induced representations, Pacific J. Math. 12 (1962), 885-911. MR 0146297 (26:3819)
  • [5] P. Hahn, Haar measure and convolution algebras on ergodic groupoids, Ph.D. Thesis, Harvard Univ., Cambridge, Mass., 1975.
  • [6] -, The regular representations of measure groupoids, Trans. Amer. Math. Soc. 242 (1978), 35-72. MR 496797 (81f:46075)
  • [7] W. Kreiger, On constructing non-$ *$-isomorphic hyperfinite factors of type III, J. Functional Analysis 6 (1970), 97-109. MR 0259624 (41:4260)
  • [8] C. Kuratowski, Topologie, Vol. 1, 4th ed., PWN, Warsaw, 1958.
  • [9] G. W. Mackey, Borel structures in groups and their duals, Trans. Amer. Math. Soc. 85 (1957), 265-311. MR 0089999 (19:752b)
  • [10] -, Ergodic theory, group theory, and differential geometry, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1184-1191. MR 0165034 (29:2325)
  • [11] -, Ergodic theory and virtual groups, Math. Ann. 166 (1966), 187-207. MR 0201562 (34:1444)
  • [12] F. J. Murray and J. von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), 116-229. MR 1503275
  • [13] A. Ramsay, Virtual groups and group actions, Advances in Math. 6 (1971), 253-322. MR 0281876 (43:7590)
  • [14] -, Boolean duals of virtual groups, J. Functional Analysis 15 (1974), 56-101. MR 0374386 (51:10586)
  • [15] M. Samuelides and J.-L. Sauvageot, Algèbre de Krieger d'un système dynamique, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), A709-A712. MR 0419735 (54:7753)
  • [16] A. K. Seda, Un concept de mesures invariantes pour les groupoïdes topologiques, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), A1603-A1605. MR 0396836 (53:696)
  • [17] J. J. Westman, Harmonic analysis on groupoids, Pacifie J. Math. 27 (1968), 621-632. MR 0244443 (39:5758)
  • [18] -, Nontransitive groupoid algebras (unpublished).
  • [19] -, Ergodic groupoid algebras and their representations (unpublished).

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28C10, 22D40

Retrieve articles in all journals with MSC: 28C10, 22D40


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0496796-6
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society