%0 Journal Article %T The regular density on the plane %A Sebastian Lindner %J Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica %D 2011 %I Krak¨®w : Wydawnictwo Naukowe Uniwersytetu Pedagogicznego %X 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. %U http://studmath.up.krakow.pl/index.php/studmath/article/view/105