Skip to main content

The use of packing measure in the analysis of random sets

Part of the Lecture Notes in Mathematics book series (LNM,volume 1203)

Keywords

  • Hausdorff Dimension
  • Hausdorff Measure
  • Packing Measure
  • Outer Measure
  • Dyadic Cube

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. J. Adler, The geometry of random fields, Wiley, 1980

    Google Scholar 

  2. K. J. Falconer, The geomtry of fractal sets, Cambridge Press, 1985.

    Google Scholar 

  3. B. B. Fristedt, Upper functions for symmetric processes with stationary independent movements, Indiana Math J. 21 (1971), 177–185.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. B. F. Fristedt and S. J. Taylor, The exact packing measure for the trajectory of a subordinator (in preparation).

    Google Scholar 

  5. J. Hawkes, Hausdorff measure, entropy, and the independence of small sets, Proc. Lon. Math. Soc. 28 (1974), 700–724.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. W. J. Hendricks, A uniform lower bound for Hausdorff dimension for transient symmetric Lévy processes, Annals of Prob. 11 (1984), 589–592.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. B. B. Mandelbrot, The fractal geometry of nature, Freeman, 1982.

    Google Scholar 

  8. W. E. Pruitt, The Hausdorff dimension of the range of a process with stationary independent increments. Jour. Math. and Mechanics 19 (1969), 371–378.

    MathSciNet  MATH  Google Scholar 

  9. W. E. Pruitt and S. J. Taylor, Sample path properties of processes with stable components, Z. Wahrscheinlichkeits-theorie, 12 (1969), 267–289.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. W. E. Puritt and S. J. Taylor, The packing dimension of the trajectory of a Lévy process (in preparation).

    Google Scholar 

  11. S. J. Taylor and C. Tricot, Packing measure and its evaluation for a Brownian path, Trans. Amer. Math. Soc. 288 (1985), 679–699.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Taylor, S.J. (1986). The use of packing measure in the analysis of random sets. In: Itô, K., Hida, T. (eds) Stochastic Processes and Their Applications. Lecture Notes in Mathematics, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076883

Download citation

  • DOI: https://doi.org/10.1007/BFb0076883

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16773-0

  • Online ISBN: 978-3-540-39852-3

  • eBook Packages: Springer Book Archive