Geodesic
The Hausdorff Dimension Distribution of Finite Measures in Euclidean Space
Canadian journal of mathematics, Tome 38 (1986) no. 6, pp. 1459-1484

Voir la notice de l'article provenant de la source Cambridge University Press

Let E be a Borel set of R N . The α-outer Hausdorff measure of E has been defined to be where and each Bi is a closed ball. d(Bi) denotes the diameter of Bi .It is easily seen that the same value Hα(E) is obtained if we consider coverings of E by open balls or by balls which may be either open or closed.By dim(E) we will mean the usual Hausdorff-Besicovitch dimension of E, where 
Cutler, Colleen D. The Hausdorff Dimension Distribution of Finite Measures in Euclidean Space. Canadian journal of mathematics, Tome 38 (1986) no. 6, pp. 1459-1484. doi: 10.4153/CJM-1986-071-9
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[1] 1. Billingsley, P., Hausdorff dimension in probability theory, Illinois Journal of Mathematics 4 (1960), 187–209. Google Scholar

[2] 2. Billingsley, P., Hausdorff dimension in probability theory II, Illinois Journal of Mathematics 5 (1961), 291–298. Google Scholar

[3] 3. Billingsley, P., Ergodic theory and information (Krieger, 1978). Google Scholar

[4] 4. Cutler, C., Some measure-theoretic and topological results for measure-valued and set-valued stochastic processes, Ph.D. Thesis, Carleton University (1984). Google Scholar

[5] 5. Gács, P., Hausdorff dimension and probability distributions, Periodica Mathematica Hungarica (Budapest) 3 (1973), 59–71. Google Scholar

[6] 6. Loève, M., Probability theory II (Springer-Verlag, 1978). Google Scholar | DOI

[7] 7. Rogers, C. A., Hausdorff measures (Cambridge University Press, 1970). Google Scholar

[8] 8. Rogers, C. A. and Taylor, S. J., The analysis of additive set functions in Euclidean space, Acta Mathematica Stockholm 101 (1959), 273–302. Google Scholar

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