P. M orters and D.Preiss, On one{sided average densities of fractal measures on the line, Seminaire d'initiation l'analyse, Publ.Univ.Pierre et Marie Curie, Paris, 1995. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Symmetry Properties of Average Densities and Tangent Measure.. - Mörters (1996) (1 citation) (Correct)
....self similarity properties. Average densities have also been used for the investigation of general measures with positive lower and nite upper densities. For example, Falconer and Springer in [6] and Marstrand in [11] generalize a classical inequality of Marstrand using average densities and in [16] it is shown that the lower one sided average densities do not vanish. In [4] Bedford and Fisher ask whether the left sided and right sided average densities always agree. An answer to this question can be given in the following form. Theorem 1.1 Suppose is a Radon measure on the line with ....
P. M orters and D.Preiss, On one{sided average densities of fractal measures on the line, Seminaire d'initiation l'analyse, Publ.Univ.Pierre et Marie Curie, Paris, 1995.
Symmetry Properties of Average Densities and Tangent Measure.. - Mörters Self-citation (Orters) (Correct)
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P. M orters and D.Preiss, On one{sided average densities of fractal measures on the line, Seminaire d'initiation l'analyse, Publ.Univ.Pierre et Marie Curie, Paris, 1995.
Tangent Measure Distributions of Fractal Measures - Mörters, Preiss Self-citation (Orters Preiss) (Correct)
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P. Morters and D. Preiss. On one{sided average densities of fractal measures on the line. Sem. d'initiation a l'analyse, Publ. Univ. Pierre et Marie Curie, Paris, 117: Expose 4, 1994/5.
Tangent Measure Distributions of Fractal Measures - Mörters, Preiss (1998) Self-citation (Preiss) (Correct)
....regularity even if the original objects are highly irregular. We believe that this improves the understanding of the geometry of non recti able sets and measures and we illustrate the strength of this result by means of several examples of its application to questions studied previously in [BeFi] [M oPr], M o2] and [FaSp] Ma2] We also remark that our result is new even on the line. However, in the important case of measures on the line with positive lower and nite upper densities it is possible to deduce the Palm property of tangent measure distributions from very detailed information about ....
.... R (U(0; 1) K)dP ( and we can employ the same argument as in Proposition 9. As an immediate corollary of these propositions we obtain the following result, which was obtained only under the additional assumption of positive lower dimensional density in [M o2] and, in a weaker form, in [M oPr]. Theorem 4. Let 0 and 2 M(R) be a measure on the line with nite upper dimensional densities almost everywhere. Then, at almost all points x, the right and left lower average dimensional densities coincide and each of them is half of the lower average dimensional density of at ....
P. Morters and D. Preiss. On one{sided average densities of fractal measures on the line. Sem. d'initiation a l'analyse, Publ. Univ. Pierre et Marie Curie, Paris, 117: Expose 4, 1994/5.
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