Skip to main content
SpringerLink
Log in

The classification of statistically recursive sets

  • Published:
Wuhan University Journal of Natural Sciences

Abstract

The main aim of this paper is to make a classification of random setsK m (ω) constructed in theorem 2. 1 and theorem 2. 1′ in [1]. We provide five criterions for the classification. Many kinds of random sets such as Hawkes constructed in [2], Graf constructed in [3] and Mauldin constructed in [4] are the special cases ofK m (ω) constructed in [1], and then these random sets belong to some model respectively according to our classification.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hu Dihe. The construction of statistically recursive sets.Wuhan Univ J of Nat Sci, 1998,3(3): 265–269

    MATH  Google Scholar 

  2. Hawkers J. Random reorderings of intervals complementary to a linear set.Quart J Math Oxford, 1984,35: 165–172

    Article  Google Scholar 

  3. Graf S. Statistically self-similar fractals.Prob Th Rel Fields, 1987,74: 357–392

    Article  MATH  MathSciNet  Google Scholar 

  4. Mauldin R D, Williams S C. Random recursive construction: asymptotic geometric and topological properties.Tran Amer Math Soc, 1986,295: 325–346

    Article  MATH  MathSciNet  Google Scholar 

  5. Rickart C E.General theory of Banach algebra. New York: Kreiger Publishing Co Inc, 1974

    Google Scholar 

  6. Hu Xiaoyu. The exact Hausdorff measure for random re-ordering of Cantor set.Science in China (Series A), 1995,38: 273–286

    MATH  Google Scholar 

  7. Hu Dihe.An introduction to random fractals. Wuhan: Wuhan Univ Press, 1996

    Google Scholar 

  8. Hutchinson J E. Fractals and self-similarty.Indiana Univ Math J, 1981,30: 713–747

    Article  MATH  MathSciNet  Google Scholar 

  9. Falconer K J. The Hausdorff dimension of self-affine fractals.Math Proc Camb Phil Soc, 1988,103: 339–350

    MATH  MathSciNet  Google Scholar 

  10. Falconer K J. The dimension of self-affine fractals II.Math Proc Comb Phil Soc, 1992,111: 169–179

    Article  MATH  MathSciNet  Google Scholar 

  11. Graf S, Mauldin R D, Williams S C. The exact Hausdorff dimension in random recursive constructions.Memoirs Amer Math Soc, 1988,38: 1–121

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematical Sciences, Wuhan University, 430072, Wuhan, China

    Hu Dihe

Authors
  1. Hu Dihe
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the National Natural Science Fundation and the Doctal Programme Fundation of China

Hu Dihe: born in May 1935, Professor

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dihe, H. The classification of statistically recursive sets. Wuhan Univ. J. Nat. Sci. 3, 270–276 (1998). https://doi.org/10.1007/BF02829973

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02829973

Key words

Search

Navigation