Measures in locally compact groups are carried by meager sets

• Autorzy: Zakrzewski P. , Zindulka O.
• Języki publikacji: EN

Abstrakty

EN

We show that for a σ-finite diffused Borel measure in a nondiscrete locally bounded topological group there is a meager set whose complement is of measure zero.

Słowa kluczowe

EN

Borel measure; residual measure; meager set; topological group

PL

miara Borela; miara szczątkowa; skromny zbiór; topologiczna grupa

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2001
• Tom: Vol. 7, nr 2
• Strony: 225--233
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Zakrzewski P.

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

autor

Zindulka O.

• Department of Mathematics, Faculty of Civil Engineering, Czech Technical University, Thâkurova 7, 160 00 Prague 6, Czech Republic

Bibliografia

• [1] Armstrong, T, Bord measures on compact groups are meager, Illinois J. Math. 25 (1981), 667-672.
• [2] Bartoszyriski, T. and Judah, H., Set Theory: On the Structure of the Real Line, A K Peters, Wellesley, Massachusetts, 1995.
• [3] Comfort, W. W., Topological groups, in Kunen and Vaughan [13], 423-501.
• [4] Costantini, C. and Zindulka, O., No normal measures in locally connected spaces, (to appear).
• [5] Proceedings of the Conference Topology and Measure II, Ernst-Moritz-Arndt- Universität, Greifewald, 1980.
• [6] Flachsmeyer, J. and Lotz, S., A survey on hyperdiffuse measures I, Proceedings of the Conference Topology and Measure I (Greifswald), Ernst-Moritz-Arndt-Universität, 1978, 87-128.
• [7] Flachsmeyer, J. and Lotz, S., A survey on hyperdiffuse measures II, Proceedings of the Conference Topology and Measure II [5], Part I, 45-74.
• [8] Flachsmeyer, J. and Lotz, S., A survey on hyperdiffuse measures III, Proceedings of the Conference Topology and Measure II [5], Part II, 31-116.
• [9] Flachsmeyer, J. and Lotz, S., Real-valued measurable cardinals, Israel Math. Conf. Proc. 6 (1993), 961-1044.
• [10] Gardner, R. J. and Pfeffer, W. F., Borel measures, in Kunen and Vaughan [13], 423-501.
• [11] Hewitt, E. and Ross, K. A., Abstract Harmonic Analysis, Vol. I, Grundlehren Math. Wiss. 115, Springer-Verlag, Berlin, 1963.
• [12] Kakutani, S. and Kodaira, K., Uber das Haarsche Mass in der lokal bikompakten Gruppe, Proc. Imp. Acad. Tokyo 20 (1944), 444-450.
• [13] Kunen, K. and Vaughan, J. E., (eds.), Handbook of Set-Theoretic Topology, North- Holland, Amsterdam, New York, Oxford, 1984.
• [14] Lotz, S., Einige Beiträge zur Theorie hyperdiffuser Maße auf topologischen Räumen, Ph.D. Thesis, Greifewald, 1975, 87-128.
• [15] Zindulka, O., Killing residual measures, J. Appl. Anal. 5(2) (1999), 265-280.
• [16] Zindulka, O., Residual measures in locally compact spaces, Topology Appl. 108 (2000), 253-265.