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The Mean Minkowski Content of Homogeneous Random Fractals

Author

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  • Martina Zähle

    (Institute of Mathematics, University of Jena, D-07743 Jena, Germany)

Abstract

Homogeneous random fractals form a probabilistic generalisation of self-similar sets with more dependencies than in random recursive constructions. Under the Uniform Strong Open Set Condition we show that the mean D -dimensional (average) Minkowski content is positive and finite, where the mean Minkowski dimension D is, in general, greater than its almost sure variant. Moreover, an integral representation extending that from the special deterministic case is derived.

Suggested Citation

  • Martina Zähle, 2020. "The Mean Minkowski Content of Homogeneous Random Fractals," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:883-:d:366088
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