Remarks on the topologies in the Lebesgue measurable sets

• Autorzy: Hejduk J. , Loranty A.
• Języki publikacji: EN

Abstrakty

EN

This paper deals with the abstract density topologies in the family of Lebesgue measurable sets generated by an operator similar to the density lower operator defined in the family of measurable sets.

Słowa kluczowe

EN

lower density operator; topology generated by some kind of density operator; topology invariant with respect to translation (multiplication)

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 3
• Strony: 655--663
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Hejduk J.

autor

Loranty A.

• Faculty Of Mathematics And Computer Science Łódź University Banacha 22 90-238 Łódź, Poland,

Bibliografia

• [1] M. Filipczak, T. Filipczak, A generalization of the density topology, Tatra Mt. Math. Publ. 34 (2006), 37–47.
• [2] M. Filipczak, J. Hejduk, On topologies associated with the Lebesgue measure, Tatra Mt. Math. Publ. 28 (2004), 187–197.
• [3] J. Hejduk, A. B. Kharazishvili, On density point with respect to von Neumann’s topology, Real Anal. Exchange 21(1) (1995–96), 278–291.
• [4] J. Hejduk, A. Loranty, On lower and semi lower density operators, Georgian Math. J. 14 (2007), 661–667.
• [5] J. Lukàs, J. Malˇy, L. Zajiček, Fine topology methods, Real Analysis and Potential Theory, Lecture Notes in Math. 1189, Springer, Berlin, 1985.
• [6] J. Oxtoby, Measure and Category, Springer, New York, 1971.
• [7] M. Terepeta, E. Wagner-Bojakowska, -density topology, Rend. Circ. Mat. Palermo 48 (1999), 451–476.
• [8] W. Wilczyński, Density Topologies, Chapter 15 in Handbook of Measure Theory, Ed. E. Pap, Elsevier 2002, 675–702.