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On the Average Box Dimensions of Typical Compact Metric Spaces

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We study the average box dimensions of typical compact metric spaces belonging the Gromov-Hausdorff space (of all compact metric spaces) equipped with the Gromov-Hausdorff metric.

Abstract

We study the average box dimensions of typical compact metric spaces belonging the Gromov-Hausdorff space (of all compact metric spaces) equipped with the Gromov-Hausdorff metric.

참고문헌 (10)

  1. K. J. Falconer, "Fractal Geometry" (1989), John Wiley & Sons, Ltd.
  2. P. Gruber, "Dimension and Structure of Typical Compact Sets, Continua and Curves", Monatsh. Math., 108, pp.149~164 (1989)
  3. G. H. Hardy, "Divergent Series" (1949)
  4. M. Jacob, "Uber die Aquivalenz der Cesaroschen und der H¨olderschen Mittel fur Integrale bei gleicher reeller Ordnung k > 0", Math. Z., 26, pp.672~682 (1927)
  5. J. Myjak, "Box and Packing Dimensions of Typical Compact Sets", Monatsh. Math., 131, pp.223~226 (2000)
  6. L. Olsen, "Average box dimensions of typical compact sets", Annales Fennici Mathematici, 44(1), pp.141~165 (2019)
  7. J. Oxtoby, "Graduate Texts in Mathematics, Vol. 2" (1971), Springer-Verlag
  8. P. Petersen, "Riemannian Geometry" (2006), Springer
  9. J. Rouyer, "Generic properties of compact metric spaces", Topology Appl., 158, pp.2140~2147 (2011)
  10. D. Stroock, "Essentials of Integration Theory for Analysis" (2011), Springer Verlag

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