Peyrière, Jacques Comparaison de deux notions de dimension. (Comparison of two notions of dimension). (French) Zbl 0608.28001 Bull. Soc. Math. Fr. 114, 97-103 (1986). A random planar set is defined à la Cantor by taking the intersection of a countable family of unions of rectangles which are flatter and flatter as their diameter tends to zero. It is established a relation which links the Hausdorff dimension of this set and its dimension associated to a pseudo-metric. Reviewer: O.Lipovan Cited in 1 ReviewCited in 4 Documents MSC: 28A35 Measures and integrals in product spaces 28A75 Length, area, volume, other geometric measure theory Keywords:random planar set; Hausdorff dimension; dimension associated to a pseudo- metric × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] BEDFORD (T. J.) . - Crinkly curves, Markov Partitions and Dimension . Ph. D. Thesis (Warwick University, U.K., 1984 ). [2] BILLINGSLEY (P.) . - Ergodic theory and information , J. Wiley, 1965 . MR 33 #254 | Zbl 0141.16702 · Zbl 0141.16702 [3] CHOLLET (A.-M.) . - Ensemble de zéros à la frontière de fonctions analytiques , Ann. Inst. Fourier, vol. 26, 1976 , p. 51-80. Numdam | MR 54 #588 | Zbl 0289.32009 · Zbl 0289.32009 · doi:10.5802/aif.600 [4] CHOLLET (A.-M.) et CHAUMAT (J.) . - Ensembles de zéros et d’interpolation à la frontière de domaines strictement pseudo-convexes , Prépubl. Orsay, 34T14. · Zbl 0601.32016 [5] LOVEJOY (S.) and SCHERTZER (D.) . - The dimension and intermittency of atmospheric dynamics , Turbulent Shear Flow, vol. 4, 1984 , p. 7-33, Ed. Launder. [6] MCMULLEN (C.) . - Nagoya Math. J., 96 ( 1984 ) p. 1. Article | Zbl 0539.28003 · Zbl 0539.28003 [7] MANDELBROT (B. B.) . - Self affine fractal sets . In Fractals in Physics (Trieste, 1985 ). Edited by L. Pietronero and E. Tosatti. North Holland Publishing Company 1986 . · Zbl 1063.28500 [8] PEYRIÈRE (J.) . - Mesures singulières associées à des découpages aléatoires d’un hypercube , Le volume de Colloquium Mathematicum en l’honneur de S. Hartman (à paraître). · Zbl 0639.60018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.