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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 91, Issue 1
  • January 1982, pp. 57-74

Two definitions of fractional dimension

  • Claude Tricot (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100059119
  • Published online: 24 October 2008
Abstract

The main properties of the Hausdorff dimension, here denoted by dim, are

In ℝp, in variance under a group Н of homeomorphisms: ∀HεH, dim О H = dim. The definition of H, introduced in (15) and (16), is recalled in § 2.

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(1)A. F. Beardon The generalized capacity of Cantor sets, Quart. J. Math. Oxford (2) 19 (1968), 301304.

(9)A. N. Kolmogorov and V. M. Tihomirov e-Entropy and e-capacity of sets in functional spaces. Amer. Math. Soc. Transl. 17 (1961), 277364.

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