Estimations de la dimension inférieure et de la dimension supérieure des mesures
Annales de l'I.H.P. Probabilités et statistiques (1998)
- Volume: 34, Issue: 3, page 309-338
- ISSN: 0246-0203
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topHeurteaux, Yanick. "Estimations de la dimension inférieure et de la dimension supérieure des mesures." Annales de l'I.H.P. Probabilités et statistiques 34.3 (1998): 309-338. <http://eudml.org/doc/77605>.
@article{Heurteaux1998,
author = {Heurteaux, Yanick},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Hausdorff measure; packing measure; Hausdorff dimension; lower and upper dimension; Cantor sets; multifractal analysis; Tricot dimension; Rényi dimensions; quasi-Bernoulli measures},
language = {fre},
number = {3},
pages = {309-338},
publisher = {Gauthier-Villars},
title = {Estimations de la dimension inférieure et de la dimension supérieure des mesures},
url = {http://eudml.org/doc/77605},
volume = {34},
year = {1998},
}
TY - JOUR
AU - Heurteaux, Yanick
TI - Estimations de la dimension inférieure et de la dimension supérieure des mesures
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1998
PB - Gauthier-Villars
VL - 34
IS - 3
SP - 309
EP - 338
LA - fre
KW - Hausdorff measure; packing measure; Hausdorff dimension; lower and upper dimension; Cantor sets; multifractal analysis; Tricot dimension; Rényi dimensions; quasi-Bernoulli measures
UR - http://eudml.org/doc/77605
ER -
References
top- [1] A. Batakis, Harmonic measure of some Cantor type sets, Ann. Acad. Sci. Fenn., vol. 21, 1996, p. 255-270. Zbl0849.31005MR1404086
- [2] A. Beurling et L. Ahlfors, The boundary correspondance under quasiconformal mappings, Acta Math., vol. 96, 1956, p. 125-142. Zbl0072.29602MR86869
- [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. Zbl0009.39503JFM60.0949.01
- [4] P. Billingsley, Ergodic theory and information, J. Wiley & Sons, Inc., New York, 1965. Zbl0141.16702
- [5] A. Bisbas, A multifractal analysis of an interesting class of measures, Colloq. Math., vol. 69, 1995, p. 37-42. Zbl0849.28003MR1341679
- [6] A. Bisbas et C. Karanikas, On the Hausdorff dimension of Rademacher Riesz products, Monatsh. Math., vol. 110, 1990, p. 15-21. Zbl0726.42016MR1072724
- [7] J. Bourgain, On the Hausdorff dimension of harmonic measure in higher dimension, Invent. Math., vol. 87, 1987, p. 477-483. Zbl0616.31004MR874032
- [8] G. Brown, G. Michon et J. Peyrière, On the Multifractal Analysis ofMeasures, J. Stat. Phys., vol. 66, 1992, p. 775-790. Zbl0892.28006MR1151978
- [9] L. Caffarelli, E. Fabes et C. Kenig, Completely singular elliptic-harmonic measures, Ind. U. Math. J., vol. 30, 1981, p. 917-924. Zbl0482.35020MR632860
- [10] L. Carleson, On the support of harmonic for sets of cantor type, Ann. Acad. Sci. Fenn., vol. 10, 1985, p. 113-123. Zbl0593.31004MR802473
- [ 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. Zbl0031.20801MR31026
- [12] K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, J. Wiley & Sons Ltd., New York, 1990. Zbl0689.28003
- [13] A.H. Fan, Décompositions de mesures et recouvrements aléatoires, Publication d'Orsay 89-03, 1989. Zbl0685.60015
- [14] A.H. Fan, Sur la dimension des mesures, Studia Math., vol. 111, 1994, p. 1-17. Zbl0805.28002
- [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. Zbl0770.35014MR1114608
- [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. Zbl0577.30017MR808433
- [17] Y. Heurteaux, Sur la comparaison des mesures avec les mesures deHausdorff, C.R. Acad. Sci., Paris, t. 321, série 1, 1995, p. 61-65. Zbl0843.28001MR1340083
- [18] R. Kaufman et J.M. Wu, Two problems on doubling measures, Rev. Mat. Iberoamericana, vol. 11, 1995, p. 527-545. Zbl0862.28005MR1363204
- [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. Zbl0551.30021MR740898
- [21] G. Michon, Mesures de Gibbs sur les cantor réguliers, Ann. Inst. H. Poincaré, Phys. Théor., vol. 58, 1983, p. 267-285. Zbl0784.60097MR1222943
- [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. Zbl0886.28006MR1402878
- [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. TricotJr, Two definitions of fractional dimension, Math. Proc. Camb. Phil. Soc., vol. 91, 1982, p. 57-74. Zbl0483.28010MR633256
- [26] P. Tukia, Hausdorff dimension and quasisymmetric mappings, Math. Scand., vol. 65, 1989, p. 152-160. Zbl0677.30016MR1051832
- [27] L. Young, Dimension, entropy and Lyapunov exponents, Ergod. Th. & Dynam. Sys., vol. 2, 1982, p. 109-124. Zbl0523.58024
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