Mesures quasi-Bernoulli au sens faible : résultats et exemples
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 1, pp. 1-35.
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     title = {Mesures {quasi-Bernoulli} au sens faible : r\'esultats et exemples},
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Testud, Benoît. Mesures quasi-Bernoulli au sens faible : résultats et exemples. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 1, pp. 1-35. doi : 10.1016/j.anihpb.2005.01.002. http://www.numdam.org/articles/10.1016/j.anihpb.2005.01.002/

[1] P. Billingsley, Ergodic Theory and Information, Wiley, New York, 1965. | MR | Zbl

[2] F. Bennasr, Analyse multifractale de mesures, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994) 807-810. | MR | Zbl

[3] F. Bennasr, I. Bhouri, Spectre multifractal de mesures boréliennes sur R d , C. R. Acad. Sci. Paris Sér. I Math. 325 (1997) 253-256. | MR | Zbl

[4] F. Bennasr, I. Bhouri, Y. Heurteaux, The validity of the multifractal formalism : results and examples, Adv. in Math. 165 (2002) 264-284. | MR | Zbl

[5] G. Brown, G. Michon, J. Peyrière, On the multifractal analysis of measures, J. Statist. Phys. 66 (1992) 775-790. | MR | Zbl

[6] K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, Wiley, New York, 1990. | MR | Zbl

[7] K. Falconer, Techniques in Fractal Geometry, Wiley, New York, 1997. | MR | Zbl

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

[9] D.J. Feng, The smoothness of L q -spectrum of self-similar measures with overlaps, J. London Math. Soc. 68 (2003) 102-118. | MR | Zbl

[10] D.J. Feng, K.S. Lau, The pressure function for products of non-negative matrices, Math. Res. Lett. 9 (2002) 363-378. | MR | Zbl

[11] D.J. Feng, K.S. Lau, Differentiability of pressure functions for products of non-negative matrices, preprint. | MR

[12] Y. Heurteaux, Sur la comparaison des mesures avec les mesures de Hausdorff, C. R Acad. Sci. Paris Sér. I Math. 321 (1995) 61-65. | MR | Zbl

[13] 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

[14] Y. Heurteaux, Weierstrass function with random phases, Trans. Amer. Math. Soc. 335 (2003) 3065-3077. | MR | Zbl

[15] J.E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J. 30 (1981) 713-747. | MR | Zbl

[16] R. Kenyon, Y. Peres, Hausdorff dimension of Sofic affine-invariant sets, Israel J. Math. 94 (1996) 127-138. | MR | Zbl

[17] K.S. Lau, S.M. Ngai, L q -spectrum of the Bernoulli convolution associated with the golden ratio, Studia Math. 131 (1998) 225-251. | MR | Zbl

[18] K.S. Lau, S.M. Ngai, Multifractal measures and a weak separation condition, Adv. in Math. 141 (1999) 45-96. | MR | Zbl

[19] G. Michon, Mesures de Gibbs sur les Cantor réguliers, Ann. Inst. H. Poincaré Phys. Théor. 58 (1983) 267-285. | Numdam | MR | Zbl

[20] C. Mcmullen, The Hausdorff dimension of general Sierpiński carpets, Nagoya Math. J. 96 (1984) 1-9. | MR | Zbl

[21] S.M. Ngai, A dimension result arising from the L q -spectrum of a measure, Proc. Amer. Math. Soc. 125 (1997) 2943-2951. | MR | Zbl

[22] S.M. Ngai, Y. Wang, Hausdorff dimension of self-similar sets with overlaps, J. London Math. Soc. 63 (2001) 655-672. | MR | Zbl

[23] E. Olivier, Communication privée.

[24] L. Olsen, A multifractal formalism, Adv. in Math. 116 (1995) 82-196. | MR | Zbl

[25] J. Peyrière, Multifractal measures, in: Proc. NATO Adv. Study Inst. Il Ciocco, vol. 372, 1997, pp. 175-186. | MR

[26] F. Przytycki, M. Urbański, On Hausdorff dimension of some fractal sets, Studia Math. 93 (1989) 155-186. | MR | Zbl

[27] M. Tamashiro, Dimensions in a separable metric space, Kyushu J. Math. 49 (1995) 143-162. | MR | Zbl

[28] B. Testud, Thèse de doctorat, Université Blaise Pascal, Clermont-Ferrand, 2004.

[29] C. Tricot, Two definitions of fractional dimension, Math. Proc. Cambridge Philos. Soc. 91 (1982) 57-74. | MR | Zbl

[30] M. Urbański, The Hausdorff dimension of the graphs of continuous self-affine functions, Proc. Amer. Math. Soc. 108 (1990) 921-930. | MR | Zbl

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