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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Packing dimension of a set is an upper bound for the packing dimensions of measures on the set. Recently the packing dimension of statistically self-similar Cantor set, which has uniform distributions for contraction ratios, was shown to be its Hausdorff dimension. We study the method to find an upper bound of packing dimensions and the upper R´enyi dimensions of measures on a statistically quasi-self-similar Cantor set (its packing dimension is still unknown) which has non-uniform distributions of contraction ratios. As results, in some statistically quasi-self-similar Cantor set we show that every probability measure on it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely and it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely for almost all probability measure on it.
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참고문헌 (10)
참고문헌 신청
/ 1973197202. / Limits for martingale like sequences
/ 1982 / Two definitions of fractional dimension
/ 1994 / A variational principle for the Hausdor dimensionsof fractal sets : 6472 ~
/ 1994 / The multifractal spectrum of statistically self-similar measures
/ 1995 / On the existence of subsets of nite positive packingmeasure 42 : 15 ~ 42
/ 1982 / Two definitions of fractional dimension
/ 1994 / A variational principle for the Hausdor dimensionsof fractal sets : 6472 ~
/ 1994 / The multifractal spectrum of statistically self-similar measures
/ 1995 / On the existence of subsets of nite positive packingmeasure 42 : 15 ~ 42
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