Estimations de la dimension inférieure et de la dimension supérieure des mesures

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 34, Issue 3, 1998, Pages 309-338

  Heurteaux, Yanick ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

Hausdorff dimension; Hausdorff measure; Lower and upper dimension; Multifractal analysis; Packing measure; Tricot dimension

Indexed keywords

EID: 0032065454     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(98)80014-9     Document Type: Article

References (27)

1. [1] A. BATAKIS, Harmonic measure of some Cantor type sets, Ann. Acad. Sci. Fenn., vol. 21, 1996, p. 255-270.
2. [2] A. BEURLING et L. AHLFORS, The boundary correspondance under quasiconformal mappings, Acta Math., vol. 96, 1956, p. 125-142.
3. [3] A. S. BESICOVITCH, On the sum of digits of real numbers represented in the dyadic system, Math. Annalen, vol. 110, 1934-35, p. 321-330.
4. [4] P. BILLINGSLEY, Ergodic theory and information, J. Wiley & Sons, Inc., New York, 1965.
5. [5] A. BISBAS, A multifractal analysis of an interesting class of measures, Colloq. Math., vol. 69, 1995, p. 37-42.
6. [6] A. BISBAS et C. KARANIKAS, On the Hausdorff dimension of Rademacher Riesz products, Monatsh. Math., vol. 110, 1990, p. 15-21.
7. [7] J. BOURGAIN, On the Hausdorff dimension of harmonic measure in higher dimension, Invent. Math., vol. 87, 1987, p. 477-483.
8. [8] G. BROWN, G. MICHON et J. PEYRIÈRE, On the Multifractal Analysis of Measures, J. Stat. Phys., vol. 66, 1992, p. 775-790.
9. [9] L. CAFFARELLI, E. FABES et C. KENIG, Completely singular elliptic-harmonic measures, Ind. U. Math. J., vol. 30, 1981, p. 917-924.
10. [10] L. CARLESON, On the support of harmonic for sets of cantor type, Ann. Acad. Sci. Fenn., vol. 10, 1985, p. 113-123.
11. [11] H. G. EGGLESTON, The fractional dimension of a set defined by decimal properties, Quart. J. Math. Oxford, Ser. (2), vol. 20, 1949, p. 31-46.
12. [12] K. FALCONER, Fractal Geometry, Mathematical Foundations and Applications, J. Wiley & Sons Ltd., New York, 1990.
13. [13] A. H. FAN, Décompositions de mesures et recouvrements aléatoires, Publication d'Orsay 89-03, 1989.
14. [14] A. H. FAN, Sur la dimension des mesures, Studia Math., vol. 111, 1994, p. 1-17.
15. [15] R. FEFFERMAN, C. KENIG et J. PIPHER, The theory of weights and the Dirichlet problem for elliptic equations, Ann. of Math. (2), vol. 134, 1991, p. 65-124.
16. [16] W. K. HAYMAN et A. HINKKANEN, Distorsion estimates for quasisymmetric functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A, vol. 36-37, 1982-83, p. 51-67.
17. [17] Y. HEURTEAUX, Sur la comparaison des mesures avec les mesures de Hausdorff, C.R. Acad. Sci., Paris, t. 321, série 1, 1995, p. 61-65.
18. [18] R. KAUFMAN et J. M. WU, Two problems on doubling measures, Rev. Mat. Iberoamericana, vol. 11, 1995, p. 527-545.
19. [19] N. MAKAROV et A. VOLBERG, On the harmonic measure of discontinous fractals, preprint LOMI E-6-86, Lenningrad, 1986.
20. [20] A. MANNING, The dimension of the maximal measure for a polynomial map, Ann. of Maths. (2), vol. 119, 1984, p. 425-430.
21. [21] G. MICHON, Mesures de Gibbs sur les cantor réguliers, Ann. Inst. H. Poincaré, Phys. Théor., vol. 58, 1983, p. 267-285.
22. q spectrum of a measure, Proc. Amer. Math. Soc., vol. 125, 1997, p. 2943-2951.
23. [23] J. PEYRIÈRE, An introduction to fractal measures and dimensions, Lectures at Xiangfan, 1995.
24. [24] C. TRICOT Jr, Sur la classification des ensembles boréliens de mesure de Lebesgue nulle, Thèse, Faculté des Sciences de l'Université de Genève, 1980.
25. [25] C. TRICOT Jr, Two definitions of fractional dimension, Math. Proc. Comb. Phil. Soc., vol. 91, 1982, p. 57-74.
26. [26] P. TUKIA, Hausdorff dimension and quasisymmetric mappings, Math. Scand., vol. 65, 1989, p. 152-160.
27. [27] L. YOUNG, Dimension, entropy and Lyapunov exponents, Ergod. Th. & Dynam. Sys., vol. 2, 1982, p. 109-124.