Journal of Theoretical Probability

, Volume 3, Issue 2, pp 169–179

Maximum and minimum sets for some geometric mean values

  • Richard E. Pfiefer

DOI: 10.1007/BF01045156

Cite this article as:
Pfiefer, R.E. J Theor Probab (1990) 3: 169. doi:10.1007/BF01045156


Ifvr is ther-dimensional volume of ther-simplex formed byr+1 points taken at random from a compact setK in ℝn, withrn, andh is a (strictly) increasing function, then the (unique) compact set that gives the minimum expected value ofh o vr, is proved to be the ellipsoid (whenr=n) and the ball (whenr<n) almost everywhere. This result is established by using a single integral inequality for centrally symmetric quasiconvex functions integrated over compact rectangles.

Key Words

Geometric mean values random simplex 

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Richard E. Pfiefer
    • 1
  1. 1.Department of Mathematics and Computer ScienceSan Jose State UniversitySan Jose

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