Limit Theorems for Probability Measures on Totally Disconnected Groups

Semigroup Forum

Volumn 58, Issue 1, 1999, Pages 69-84

  Telöken, Klaus ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013301663     PISSN: 00371912     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002339900009     Document Type: Article

References (33)

1. Billingsley, P., "Convergence of Probability Measures", Wiley, New York, 1968.
2. Billingsley, P., Convergence of types in k-spaces, Z. Wahrsch. verw. Gebiete 5 (1966), 175-179.
3. Borel, A., "Groupes linéaires algébriques", Ann. Math., II 64 (1956), 20-82.
4. Borel, A., "Linear Algebraic Groups", Benjamin, 1969.
5. Bourbaki, N., "Intégration", volume VI, Hermann, Paris, 1963.
6. Bourbaki, N., "Algebra", volume II, Addison-Wesley, New York, 1974.
7. Dani, S. G. and M. McCrudden, On the factor sets of measures and local tightness of convolution semigroups over Lie groups, J. Theor. Prob, 1 (1988), 357-370
8. Dugundji, J., "Topology", Allyn and Bacon, Boston London Sydney Toronto, 1966.
9. Hazod, W., "Stetige Halbgruppen von Wahrscheinlichkeitsmaßen und erzeugende Distributionen", Springer Verlag, 1977.
10. Hazod W., Remarks on [semi]-stable probabilities, In Heyer, editor, Proceedings Oberwolfach, Lecture Notes in Mathematics, Springer Verlag 1064 (1983), 182-203.
11. Hazod, W. and H. P. Scheffler, The domains of partial attraction of probabilities on groups and on vector spaces, J. Theor. Prob. 6 (1993), 175-186.
12. Heyer, H., "Probability measures on locally compact groups", Springer-Verlag, 1977.
13. Hochschild, G., "The structure of Lie groups", Holden Day, San Francisco-London-Amsterdam, 1965.
14. Hochschild, G., "Basic Theory of Algebraic Groups and Lie Algebras", Springer Verlag, 1981.
15. Hewitt, E. and K. A. Ross, "Abstract harmonic analysis", volume 1, Springer Verlag, 1963.
16. Humphreys, J. E., "Linear Algebraic Groups", Springer Verlag, 1975.
17. Khokhlov, Y. S., Stable distributions and their generalizations: Structure and limit theorem, In: Proceedings Oberwolfach XI, 1995, World Scientific, Singapore New Jersey London Hong Kong, 210-224.
18. Kruglov, V. M., On an extension of the class of stable distributions., Theory Prob. Appl. 17 (1972), 723-732.
19. Mukherjea, A., Limit theorems for probability measures on non-compact groups and semigroups, Z. Wahrsch. verw. Gebiete 33 (1976), 273-284.
20. Müller-Römer, P. R., Kontrahierbare Erweiterungen und kontrahierbare Gruppen, J. Reine Angew. Math. 283/284 (1976), 238-264.
21. Neuenschwander, D. and H. P. Scheffler, Laws of the iterated logarithm for the central part of [semi-]stable measures on the Heisenberg groups, Monatsheft Math., to appear.
22. Nobel, S., Limit theorems for probability measures on simply connected nilpotent Lie groups., J. Theor. Prob. 4 (1991), 261-284.
23. Nobel, S., "Grenzwertsätze für Wahrscheinlichkeitsmaße auf einfach zusammenhängenden nilpotenten Liegruppen", Dissertation, Universität Dortmund, 1988.
24. Pillai, R. N., Semistable laws as limit distributions, Ann. Math. Stat. 42 (1971), 780-783.
25. Scheffler, H. P., "Anziehungsbereiche stabiler Wahrscheinlichkeitsmaße auf stratifizierbaren Liegruppen" Dissertation, Universität Dortmund, 1992.
26. Shah, R., Convergence-of-types theorems on p-adic algebraic groups, In: Proceedings Oberwolfach XI, 1995, World Scientific, Singapore New Jersey London Hong Kong, 357-363.
27. Shah, R., Infinitely divisible measures on p-adic groups, J. Theor. Prob. 4 (1991), 391-405.
28. Shah, R., Semistable measures and limit theorems on real and p-adic groups, Monatshefte Math. 115 (1993), 191-213.
29. Siebert, E., Contractive automorphisms on locally compact groups, Math. Z. 191 (1986), 73-90.
30. Taibleson, M. H., "Fourier Analysis on Local Fields", Princeton University Press, 1975.
31. Telöken, K., "Grenzwertsätze für Wahrscheinlichkeitsmaße auf total unzusammenhängenden Gruppen", Dissertation, Universität Dortmund, 1996.
32. Telöken, K., A convergence-of-types theorem for contractible groups, unpublished manuscript.
33. Wang, S. P., The Mautner phenomenon for p-adic Lie groups, Math. Z. 185 (1984), 403-411.