The regular density on the plane

Sebastian Lindner

Abstract


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.

Keywords


O'Malley points; density; variation

Mathematics Subject Classification


26A45

References


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.


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