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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generic properties of compact starshaped sets
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by Peter M. Gruber and Tudor I. Zamfirescu PDF
Proc. Amer. Math. Soc. 108 (1990), 207-214 Request permission

Abstract:

A typical compact starshaped set in ${{\text {E}}^d}$ is "small" from the topological as well as from the measure theoretic viewpoint. We formulate this more explicitly in the paper by using the notions of porosity and Hausdorff dimension. Moreover, we see that the directions of the line segments in a typical compact starshaped set are many, but not too many.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 108 (1990), 207-214
  • MSC: Primary 52A30; Secondary 54E52
  • DOI: https://doi.org/10.1090/S0002-9939-1990-0986649-X
  • MathSciNet review: 986649