Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE CENTERED-NET MEASURES AND THEIR REGULAR SETS

  • T. H (Mathematics Department, Kyungpook National University) ;
  • S. P (Mathematics Dept, Kyungpook National University) ;
  • H. H (Mathematics Dept, Pohang Univ of Science Technology)
  • Published : 2000.05.01

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Abstract

We define the centered-net covering and the centered-net parking measure and then show that the regular sets induced by the two centered measures are equal for $C{\frac}{\delta}{R}$ almost everywhere.

Keywords

References

  1. Techniques in Fractal Geometry K. Falconer
  2. Hiroshima Math. J. v.25 On the Billingsley dimension on $R^N$ S. Ikeda
  3. Korean J. Math. Sciences v.4 The densities for net packing measure Tae Hee Kim;Hung Hwan Lee
  4. Kyungpook Math. J. v.37 The Nets and Packing Dimension Tae Hee Kim;Hung Hwan Lee
  5. Geometry of sets and Measures in Euclidean Spaces P. Mattila
  6. Trans. Amer. Math. soc. v.113 The (ø,s)-regular subsets of n-space J. M. Marstrand
  7. Annals of Mathematics v.125 Geometry of measures in $R^n$: distribution, rectifiability and densities D. Preiss
  8. Math. Proc. Phil. Soc. v.103 Packing regularity of sets in n-space X. Raymond;C. Tricot
  9. Trans. Amer. Math. Soc. v.288 Packing measure and its evaluation for Brownian paths S. J. Taylor;C. Tricot
  10. Math. Proc. Cam. Phil. Soc. v.99 The packing measure of rectifiable of subsets of the plane S. J. Taylor;C. Tricot
  11. Math. Proc. Cam. Phil. Soc. v.91 Two definitions of fractional dimension C. Tricot