Let be a self-similar set with similarities ratio and Hausdorff dimension , let be a probability vector. The Besicovitch-type subset of is defined as
Soit un ensemble auto-similaire avec coefficients de similarité et de dimension de Hausdorff , et soit un vecteur de probabilité. Le sous-ensemble de type de Besicovitch de est défini par
Keywords: perturbation measures, gauge functions, Besicovitch set
Mot clés : mesures de perturbation, fonctions de jauge, ensemble de Besicovitch
Ma, Ji-Hua 1; Wen, Zhi-Ying 2; Wu, Jun 1
@article{AIF_2002__52_4_1061_0, author = {Ma, Ji-Hua and Wen, Zhi-Ying and Wu, Jun}, title = {Besicovitch subsets of self-similar sets}, journal = {Annales de l'Institut Fourier}, pages = {1061--1074}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {52}, number = {4}, year = {2002}, doi = {10.5802/aif.1911}, zbl = {1024.28005}, mrnumber = {1926673}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1911/} }
TY - JOUR AU - Ma, Ji-Hua AU - Wen, Zhi-Ying AU - Wu, Jun TI - Besicovitch subsets of self-similar sets JO - Annales de l'Institut Fourier PY - 2002 SP - 1061 EP - 1074 VL - 52 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1911/ DO - 10.5802/aif.1911 LA - en ID - AIF_2002__52_4_1061_0 ER -
%0 Journal Article %A Ma, Ji-Hua %A Wen, Zhi-Ying %A Wu, Jun %T Besicovitch subsets of self-similar sets %J Annales de l'Institut Fourier %D 2002 %P 1061-1074 %V 52 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1911/ %R 10.5802/aif.1911 %G en %F AIF_2002__52_4_1061_0
Ma, Ji-Hua; Wen, Zhi-Ying; Wu, Jun. Besicovitch subsets of self-similar sets. Annales de l'Institut Fourier, Volume 52 (2002) no. 4, pp. 1061-1074. doi : 10.5802/aif.1911. https://aif.centre-mersenne.org/articles/10.5802/aif.1911/
[1] On the sum of digits of real numbers represented in the dyadic system, Math. Ann, Volume 110 (1934), pp. 321-330 | DOI | JFM | MR | Zbl
[2] The fractional dimension of a set defined by decimal properties, Quart. J. Math. Oxford Ser, Volume 20 (1949), pp. 31-36 | DOI | MR | Zbl
[3] Techniques in Fractal Geometry, John Wiley and sons inc., 1997 | MR | Zbl
[4] A further example on scales of Hausdorff functions, J. London Math. Soc, Volume 8 (1974) no. 2, pp. 585-586 | DOI | MR | Zbl
[5] Singularity of self-similar measures with respect to Hausdorff measures, Trans. of Amer. Math. Soc., Volume 350 (1998) no. 6, pp. 2297-2310 | DOI | MR | Zbl
[6] The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure, Math. Proc. Camb. Phil. Soc, Volume 116 (1994), pp. 513-526 | DOI | MR | Zbl
[7] Probability, Springer-Verlag, New York, 1984 | MR | Zbl
[8] The measure theory of random fractals, Math. Proc. Cambridge Philo. Soc, Volume 100 (1986), pp. 383-408 | DOI | MR | Zbl
Cited by Sources: