The regular density on the plane

Sebastian Lindner


In the note [1] the notion of the regular density point of the measurable subset of the real line was introduced. Then it was shown that the new definition is equivalent to the definition of O'Malley points, which has been examined in [2]. In this note we demonstrate that the analogous definitions for measurable subsets of the plane are not equivalent.


O'Malley points; density; variation

Mathematics Subject Classification



Lindner, S. and W. Wilczyński. "On points of the regular density." Tatra Mt. Math. Publ. 52 (2012): 9-17.

Poreda, W. and W. Wilczyński. "Topology similar to the density topology." Bull. Soc. Sci. Lett. Łódź Sér. Rech. Déform. 34 (2001): 55-60.

Full Text: PDF

Download statistics: 2158

e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej