The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)
- Volume 11 Issue 1
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- Pages.51-61
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- 2004
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- 1226-0657(pISSN)
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- 2287-6081(eISSN)
ON A QUASI-SELF-SIMILAR MEASURE ON A SELF-SIMILAR SET ON THE WAY TO A PERTURBED CANTOR SET
- Baek, In-Soo (Departmen tof Mathematics, Pusan University of Foreign Studies)
- Published : 2004.02.01
Abstract
We find an easier formula to compute Hausdorff and packing dimensions of a subset composing a spectral class by local dimension of a self-similar measure on a self-similar Cantor set than that of Olsen. While we cannot apply this formula to computing the dimensions of a subset composing a spectral class by local dimension of a quasi-self-similar measure on a self-similar set on the way to a perturbed Cantor set, we have a set theoretical relationship between some distribution sets. Finally we compare the behaviour of a quasi-self-similar measure on a self-similar Cantor set with that on a self-similar set on the way to a perturbed Cantor set.