2017
DOI: 10.1016/j.jmaa.2017.06.009
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Lower dimensions of some fractal sets

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Cited by 5 publications
(4 citation statements)
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“…It follows from the dimension formulae of Cantor sets [2,4] that for any θ ∈ (0, 1), we get . Let δ k be the maximal length of k-th basic interval, then we have…”
Section: 3mentioning
confidence: 97%
See 2 more Smart Citations
“…It follows from the dimension formulae of Cantor sets [2,4] that for any θ ∈ (0, 1), we get . Let δ k be the maximal length of k-th basic interval, then we have…”
Section: 3mentioning
confidence: 97%
“…To avoid some 'strange' sets whose lower Assouad type dimensions are 0 or ∞, we are mainly concerned with the uniformly perfect sets in doubling metric spaces. 2 In this paper, we study the behaviours of lower Assouad spectrum as θ ∈ (0, 1), and discuss the relationship among the lower Assouad type dimensions. Our first result is stated as follows.…”
Section: Introductionmentioning
confidence: 99%
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“…In general, since the lower dimension does not have the monotone property and the finitely stable property, it is alway difficult to do the study of the lower dimensions for fractal sets. Chen, Wu, Wei [15] discussed the lower dimensions for some Moran sets. Chen [10] , Yang, Li and Hu [16] obtained some results of the lower dimension formulas for some Moran cut-out sets and some homogeneous Moran sets.…”
Section: Introductionmentioning
confidence: 99%