Estimations de la dimension inférieure et de la dimension supérieure des mesures
Heurteaux, Yanick
Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998), p. 309-338 / Harvested from Numdam
@article{AIHPB_1998__34_3_309_0,
     author = {Heurteaux, Yanick},
     title = {Estimations de la dimension inf\'erieure et de la dimension sup\'erieure des mesures},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {34},
     year = {1998},
     pages = {309-338},
     mrnumber = {1625871},
     zbl = {0903.28005},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPB_1998__34_3_309_0}
}
Heurteaux, Yanick. Estimations de la dimension inférieure et de la dimension supérieure des mesures. Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) pp. 309-338. http://gdmltest.u-ga.fr/item/AIHPB_1998__34_3_309_0/

[1] A. Batakis, Harmonic measure of some Cantor type sets, Ann. Acad. Sci. Fenn., vol. 21, 1996, p. 255-270. | MR 1404086 | Zbl 0849.31005

[2] A. Beurling et L. Ahlfors, The boundary correspondance under quasiconformal mappings, Acta Math., vol. 96, 1956, p. 125-142. | MR 86869 | Zbl 0072.29602

[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. | JFM 60.0949.01 | Zbl 0009.39503

[4] P. Billingsley, Ergodic theory and information, J. Wiley & Sons, Inc., New York, 1965. | Zbl 0141.16702

[5] A. Bisbas, A multifractal analysis of an interesting class of measures, Colloq. Math., vol. 69, 1995, p. 37-42. | MR 1341679 | Zbl 0849.28003

[6] A. Bisbas et C. Karanikas, On the Hausdorff dimension of Rademacher Riesz products, Monatsh. Math., vol. 110, 1990, p. 15-21. | MR 1072724 | Zbl 0726.42016

[7] J. Bourgain, On the Hausdorff dimension of harmonic measure in higher dimension, Invent. Math., vol. 87, 1987, p. 477-483. | MR 874032 | Zbl 0616.31004

[8] G. Brown, G. Michon et J. Peyrière, On the Multifractal Analysis of Measures, J. Stat. Phys., vol. 66, 1992, p. 775-790. | MR 1151978 | Zbl 0892.28006

[9] L. Caffarelli, E. Fabes et C. Kenig, Completely singular elliptic-harmonic measures, Ind. U. Math. J., vol. 30, 1981, p. 917-924. | MR 632860 | Zbl 0482.35020

[10] L. Carleson, On the support of harmonic for sets of cantor type, Ann. Acad. Sci. Fenn., vol. 10, 1985, p. 113-123. | MR 802473 | Zbl 0593.31004

[ 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. | MR 31026 | Zbl 0031.20801

[12] K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, J. Wiley & Sons Ltd., New York, 1990. | Zbl 0689.28003

[13] A.H. Fan, Décompositions de mesures et recouvrements aléatoires, Publication d'Orsay 89-03, 1989. | Zbl 0685.60015

[14] A.H. Fan, Sur la dimension des mesures, Studia Math., vol. 111, 1994, p. 1-17. | Zbl 0805.28002

[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. | MR 1114608 | Zbl 0770.35014

[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. | MR 808433 | Zbl 0577.30017

[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. | MR 1340083 | Zbl 0843.28001

[18] R. Kaufman et J.M. Wu, Two problems on doubling measures, Rev. Mat. Iberoamericana, vol. 11, 1995, p. 527-545. | MR 1363204 | Zbl 0862.28005

[19] N. Makarov et A. Volberg, On the harmonic measure of discontinous fractals, preprint LOMI E-6-86, Lenningrad, 1986.

[20] A. Manning, The dimension of the maximal measure for a polynomial map, Ann. of Maths. (2), vol. 119, 1984, p. 425-430. | MR 740898 | Zbl 0551.30021

[21] G. Michon, Mesures de Gibbs sur les cantor réguliers, Ann. Inst. H. Poincaré, Phys. Théor., vol. 58, 1983, p. 267-285. | Numdam | MR 1222943 | Zbl 0784.60097

[22] S.M. Ngai, A dimension result arising from the Lq spectrum of a measure, Proc. Amer. Math. Soc., vol. 125, 1997, p. 2943-2951. | MR 1402878 | Zbl 0886.28006

[23] J. Peyrière, An introduction to fractal measures and dimensions, Lectures at Xiangfan, 1995.

[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] C. Tricot Jr, Two definitions of fractional dimension, Math. Proc. Camb. Phil. Soc., vol. 91, 1982, p. 57-74. | MR 633256 | Zbl 0483.28010

[26] P. Tukia, Hausdorff dimension and quasisymmetric mappings, Math. Scand., vol. 65, 1989, p. 152-160. | MR 1051832 | Zbl 0677.30016

[27] L. Young, Dimension, entropy and Lyapunov exponents, Ergod. Th. & Dynam. Sys., vol. 2, 1982, p. 109-124. | Zbl 0523.58024