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Two definitions of fractional dimension

  • Claude Tricot (a1)

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)Beardon, A. F.The generalized capacity of Cantor sets, Quart. J. Math. Oxford (2) 19 (1968), 301304.
(2)Besicovitch, A. S. and Moban, P. A. P.The measure of product and cylinder sets. J. London Math. Soc. 20 (1945), 110120.
(3)Billingsley, P.Hausdorff dimension in probability theory. Illinois J. Math. 4 (1960), 187209.
(4)Davies, R. O.Subsets of finite measure in analytic sets. Indagat. Math. 14 (1952), 488489.
(5)Eggileston, H. G.A correction to a paper on the dimension of cartesian product sets. Proc. Camb. Phil. Soc. 49 (1953), 437440.
(6)Hawkes, J.Hausdorff measure, entropy, and the independence of small sets. Proc. London Math. Soc. (3) 28 (1974), 700724.
(7)Kahane, J. P. et Salem, R.Ensembles parfaits et series trigonométriques. Paris, Hermann, 1963.
(8)Kaufman, R.On Hausdorff dimension of projections. Mathematika 15 (1968), 153155.
(9)Kolmogorov, A. N. and Tihomirov, V. M.e-Entropy and e-capacity of sets in functional spaces. Amer. Math. Soc. Transl. 17 (1961), 277364.
(10)Larman, D. G.On Hausdorff measure in finite-dimensional compact metric spaces. Proc. London Math. Soc. (3), 17 (1967), 193206.
(11)Marstrand, J. M.The dimension of the cartesian product sets. Proc. Camb. Phil. Soc. 50 (1954), 198202.
(12)Rogers, C. A.Hausdorff measures. Cambridge University Press, 1970.
(13)Rogers, C. A. and Taylor, S. J.Additive set functions in euclidean space. Ada Math. 101 (1959), 273302.
(14)Tricot, C. Sur la notion de densité. Cahiers du Dep. d'Econométrie de l'Université de Genève (1973).
(15)Tricot, C. JrSur la classification des ensembles boré liens de measure de Lebesgue nulle. Genève, Imprimerie Nationale, 1980.
(16)Tricot, C. JrRarefaction indices. Mathematika 27 (1980), 4657.
(17)Wegmann, H.Die Hausdorff-Dimension von kartesischen Produktmengen in metrischen Räumen. J. Reine Angew. Math. 234 (1969), 163171.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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