Monotone measures with bad tangential behavior in the plane

0374114 - MÚ 2012 RIV CZ eng J - Článek v odborném periodiku
Černý, R. - Kolář, Jan - Rokyta, M.
Monotone measures with bad tangential behavior in the plane.
Commentationes Mathematicae Universitatis Carolinae. Roč. 52, č. 3 (2011), s. 317-339. ISSN 0010-2628
Grant CEP: GA AV ČR IAA100190903
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: monotone measure * monotonicity formula * tangent measure
Kód oboru RIV: BA - Obecná matematika
http://www.dml.cz/handle/10338.dmlcz/141604

We show that for every epsilon > 0, there is a set A in R2 such that the Hausdorff one dimensional measure restricted to A is a monotone measure, the corresponding tangent measures at the origin are not unique and the measure has the 1-dimensional density between 1 and 3+epsilon everywhere on the support.
Trvalý link: http://hdl.handle.net/11104/0207114