The regular density on the plane
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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