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Geometric theories of measure and area

  • Peter Mani-Levitska

Abstract

Although there are a number of different methods to define the volume, or the surface area, for a convex body K in the n-dimensional Euclidean space Rn, the values resulting from these constructions all coincide. Every reasonable definition of the volume, for example, leads to the Jordan content of K. This situation changes as soon as one starts studying the finer structure of K. Which is the natural measure for the shadow boundary of K in a given direction, or for the m-skeleton of K?

Keywords

Convex Body Geometric Theory Hausdorff Measure Multiplicity Function Lebesgue Area 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 1979

Authors and Affiliations

  • Peter Mani-Levitska
    • 1
  1. 1.Mathematisches InstitutUniversität BernBernSwitzerland

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