On the Lebesgue density theorem

• Autorzy: Wilczyński W.
• Języki publikacji: EN

Abstrakty

EN

The classical Lebesgue density theorem says that almost each point of a measurable set A is a density point of A. It is well known that the density point of a measurable set A can be described in terms of the convergence in measure of a sequence of characteristic functions of sets similar to A. In this note it is shown that in the Lebesgue density theorem the convergence in measure cannot be replaced by the convergence almost everywhere.

Słowa kluczowe

EN

density point; Lebesgue density theorem; convergence almost everywhere and in measure

PL

punkt gęstości; twierdzenie Lebesgue'a o punktach gęstości; zbieżność prawie wszędzie; zbieżność według miary

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2012
• Tom: Vol. 18, nr 2
• Strony: 275--281
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Wilczyński W.

• Faculty of Mathematics and Computer Science, Łódź University, ul. Banacha 22, 90-238 Łódź, Poland,

Bibliografia

• [1] V. Aversa and W. Wilczyński, Simple density topology, Rend. Circ. Mat. Palermo (2) 53 (2004), 344-352.
• [2] W. Poreda, E. Wagner-Bojakowska and W. Wilczyński, A category analogue of the density topology, Fund. Math. 125 (1985), 167-173.
• [3] S. J. Taylor, On strengthening the Lebesgue density theorem, Fund. Math. 46 (1959), 305-315.
• [4] S. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York, 1960.