A continuity property of the dimension of the harmonic measure of Cantor sets under perturbations
Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 1, pp. 87-107. 
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     author = {Batakis, Athanassios},
     title = {A continuity property of the dimension of the harmonic measure of {Cantor} sets under perturbations},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {87--107},
     publisher = {Gauthier-Villars},
     volume = {36},
     number = {1},
     year = {2000},
     mrnumber = {1743091},
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     url = {http://archive.numdam.org/item/AIHPB_2000__36_1_87_0/}
}
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Batakis, Athanassios. A continuity property of the dimension of the harmonic measure of Cantor sets under perturbations. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 1, pp. 87-107. http://archive.numdam.org/item/AIHPB_2000__36_1_87_0/

[1] A. Ancona, Principe de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine Lipschitzien, Annales de l' Institut Fourier, Grenoble 28 (4) (1978) 169-213. | Numdam | MR | Zbl

[2] Z. Balogh, I. Popovici and A. Volberg, Conformally maximal polynomial-like dynamics and invariant harmonic measure, Ergodic Theory Dynamical Systems 17 (1) (1997) 1-27. | MR | Zbl

[3] A. Batakis, Harmonic measure of some Cantor type sets, Ann. Acad. Sci. Fenn. 21 (1996) 255-270. | MR | Zbl

[4] A. Batakis, Théorie du potentiel : 1. Sur les domaines Poissoniens 2. Sur la mesure harmonique des ensembles de Cantor, Ph.D. Thesis, Université de Paris-Sud, 1997.

[5] A. Batakis and Y. Heurteaux, On relations between entropy and Hausdorff dimension of measures, Preprint, Prépublications d'Orsay, 1998. | MR

[6] A. Beardon, On the Hausdorff dimension of general Cantor sets, Proc. Cambridge Philos. Soc. 61 (1965) 679-694. | MR | Zbl

[7] L. Carleson, On the support of harmonic measure for sets of Cantor type, Ann. Acad. Sci. Fenn. 10 (1985) 113-123. | MR | Zbl

[8] A.H. Fan, Sur la dimension des mesures, Studia Math. 111 (1994) 1-17. | Zbl

[9] P. Hall and C.C. Heyde, Martingale Theory and its Applications, Probability and Mathematical Statistics, Academic Press, New York, 1980. | MR | Zbl

[10] Y. Heurteaux, Estimations de la dimension inférieure et de la dimension supérieure des mesures, Ann. Inst. H. Poincaré Probab. Statist. 34 (1998) 309-338. | Numdam | MR | Zbl

[11] M. Lyubich and A. Volberg, A comparison of harmonic and balanced measures on Cantor repellors, J. Fourier Analysis and Applications (Special Issue J.-P. Kahane) (1995) 379-399. | Zbl

[12] N. Makarov and A. Volberg, On the harmonic measure of discontinuous fractals, Preprint LOMI E-6-86, Leningrad, 1986.

[13] P. Mattila, Geometric Measure Theory, Cambridge University Press, 1995. | MR

[14] A. Volberg, On harmonic measure of self-similar sets in the plane, in: Harmonic Analysis and Discrete Potential Theory, Plenum Press, 1992. | MR

[15] A. Volberg, On the dimension of harmonic measure of Cantor-type repellers, Michigan Math. J. 40 (1993) 239-258. | MR | Zbl

[16] M. Zinsmeister, Formalisme Thermodynamique et Systèmes Dynamiques Holomorphes. Panoramas et Synthèses, Vol. 4, Société Mathématique de France, 1997. | MR | Zbl