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HAUSDORFF MEASURES OF A CLASS OF MORAN SETS.
- Source :
-
Fractals . May2020, Vol. 28 Issue 3, pN.PAG-N.PAG. 12p. - Publication Year :
- 2020
-
Abstract
- Let ℳ (n , c) be the class of Moran sets with integer n ≥ 2 and real c satisfying n c < 1. It is well known that the Hausdorff dimension of any set in this class is s = − log c n. We show that for any E ∈ ℳ (n , c) , 2 s 2 (n − 1) c 1 − c s ≤ ℋ s (E) ≤ 1 , where ℋ s (E) denotes s -dimensional Hausdorff measure of E. For any a with 2 s 2 (n − 1) c 1 − c s ≤ a ≤ 1 , there exists a self-similar set E ∈ ℳ (n , c) such that ℋ s (E) = a. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HAUSDORFF measures
*FRACTAL dimensions
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 0218348X
- Volume :
- 28
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Fractals
- Publication Type :
- Academic Journal
- Accession number :
- 143472882
- Full Text :
- https://doi.org/10.1142/S0218348X2050053X