Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-29T20:59:59.377Z Has data issue: false hasContentIssue false
  • English
  • Français

Tangent measures of non-doubling measures

Published online by Cambridge University Press:  13 December 2011

TUOMAS ORPONEN  and
TUOMAS SAHLSTEN
TUOMAS ORPONEN
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, P.O.B. 68, 00014 Helsinki, Finland. e-mail: [email protected], [email protected]
TUOMAS SAHLSTEN
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, P.O.B. 68, 00014 Helsinki, Finland. e-mail: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We construct a non-doubling measure on the real line, all tangent measures of which are equivalent to Lebesgue measure.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 152 , Issue 3 , May 2012 , pp. 555 - 569
Copyright
Copyright © Cambridge Philosophical Society 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Eckmann, J-P., Järvenpää, E. and Järvenpää, M.Porosities and dimensions of measures. Nonlinearity 13 (2000), 1–18.CrossRefGoogle Scholar
[2]Falconer, K. J.Fractal Geometry: Mathematical Foundations and Applications (John-Wiley & Sons Ltd 2003).CrossRefGoogle Scholar
[3]Freedman, D. and Pitman, J.A measure which is singular and uniformly locally uniform. Proc. Amer. Math. Soc. 108 (1990), 371–381.CrossRefGoogle Scholar
[4]Mattila, P.Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability (Cambridge University Press, 1995).CrossRefGoogle Scholar
[5]Mera, M. E. and Morán, M.Attainable values for upper porosities of measures. Real Anal. Exchange 26 (2001), 101–116.CrossRefGoogle Scholar
[6]Mera, M. E., Morán, M., Preiss, D. and Zajíček, L.Porosity, σ-porosity and measures. Nonlinearity 16 (2003), 493–512.CrossRefGoogle Scholar
[7]Preiss, D.Geometry of measures in ℝd: distribution, rectifiability, and densities. Ann. of Math. 125 vol. 3 (1987), 537–643.CrossRefGoogle Scholar
[8]Suomala, V.Upper porous measures on metric spaces. Illinois J. Math. 52 vol. 3 (2009), 967–980.Google Scholar