Packing dimension of mean porous measures
2009; Wiley; Volume: 80; Issue: 2 Linguagem: Inglês
10.1112/jlms/jdp040
ISSN1469-7750
AutoresD. Beliaev, Esa Järvenpää, Maarit Järvenpää, Antti Käenmäki, Tapio Rajala, Stanislav Smirnov, Ville Suomala,
Tópico(s)Analytic Number Theory Research
ResumoJournal of the London Mathematical SocietyVolume 80, Issue 2 p. 514-530 Articles Packing dimension of mean porous measures D. Beliaev, D. Beliaev Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA, [email protected]Search for more papers by this authorE. Järvenpää, Corresponding Author E. Järvenpää [email protected] Department of Mathematical Sciences, Pentti Kaiteran katu 1, PO Box 3000, 90014 University of Oulu, Finland[email protected]Search for more papers by this authorM. Järvenpää, M. Järvenpää Department of Mathematical Sciences, Pentti Kaiteran katu 1, PO Box 3000, 90014 University of Oulu, Finland, [email protected]Search for more papers by this authorA. Käenmäki, A. Käenmäki Department of Mathematics and Statistics, PO Box 35 (MaD), 40014 University of Jyväskylä, Finland, [email protected]Search for more papers by this authorT. Rajala, T. Rajala Department of Mathematics and Statistics, PO Box 35 (MaD), 40014 University of Jyväskylä, Finland, [email protected]Search for more papers by this authorS. Smirnov, S. Smirnov Department of Mathematics, University of Geneva, 2-4 rue du Lièvre, Case postale 64, 1211 Genève 4, Switzerland, [email protected]Search for more papers by this authorV. Suomala, V. Suomala Department of Mathematics and Statistics, PO Box 35 (MaD), 40014 University of Jyväskylä, Finland, [email protected]Search for more papers by this author D. Beliaev, D. Beliaev Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA, [email protected]Search for more papers by this authorE. Järvenpää, Corresponding Author E. Järvenpää [email protected] Department of Mathematical Sciences, Pentti Kaiteran katu 1, PO Box 3000, 90014 University of Oulu, Finland[email protected]Search for more papers by this authorM. Järvenpää, M. Järvenpää Department of Mathematical Sciences, Pentti Kaiteran katu 1, PO Box 3000, 90014 University of Oulu, Finland, [email protected]Search for more papers by this authorA. Käenmäki, A. Käenmäki Department of Mathematics and Statistics, PO Box 35 (MaD), 40014 University of Jyväskylä, Finland, [email protected]Search for more papers by this authorT. Rajala, T. Rajala Department of Mathematics and Statistics, PO Box 35 (MaD), 40014 University of Jyväskylä, Finland, [email protected]Search for more papers by this authorS. Smirnov, S. Smirnov Department of Mathematics, University of Geneva, 2-4 rue du Lièvre, Case postale 64, 1211 Genève 4, Switzerland, [email protected]Search for more papers by this authorV. Suomala, V. Suomala Department of Mathematics and Statistics, PO Box 35 (MaD), 40014 University of Jyväskylä, Finland, [email protected]Search for more papers by this author First published: 14 August 2009 https://doi.org/10.1112/jlms/jdp040Citations: 6 2000 Mathematics Subject Classification 28A75, 28A80. E.J., M.J., A.K., T.R. and V.S. acknowledge the support of the Academy of Finland (projects # 211229 and # 114821) and the Centre of Excellence in Analysis and Dynamics Research. D.B., E.J. and S.S. acknowledge the support of the Swiss National Science Foundation. T.R. appreciates the financial support of Vilho, Yrjö and Kalle Väisälä Foundation. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract We prove that the packing dimension of any mean porous Radon measure on ℝd may be estimated from above by a function which depends on mean porosity. The upper bound tends to d − 1 as mean porosity tends to its maximum value. This result was stated in D. B. Beliaev and S. K. Smirnov ['On dimension of porous measures', Math. Ann. 323 (2002) 123–141], and in a weaker form in E. Järvenpää and M. Järvenpää ['Porous measures on ℝn: local structure and dimensional properties', Proc. Amer. Math. Soc. (2) 130 (2002) 419–426], but the proofs are not correct. Quite surprisingly, it turns out that mean porous measures are not necessarily approximable by mean porous sets. We verify this by constructing an example of a mean porous measure μ on ℝ such that μ(A) = 0 for all mean porous sets A ⊂ ℝ. Citing Literature Volume80, Issue2October 2009Pages 514-530 RelatedInformation
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