• Herbert Heyer
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 94)


The idea of studying probability measures on spheres in Euclidean space ℝ p rather than on the Euclidean space itself is as old as the beginnings of probability theory and statistics. In 1734 Daniel Bernoulli looked at the orbital planes of the planes known at his time as random points on the surface of a sphere and asserted their uniform distribution. In the first quarter of this century Rayleigh and Karl Pearson started investigations on the resultant length of normal vectors, in connection with approximation problems for large samples, within the framework of random walks on spheres. Until then the distributions appearing in the work of the pioneers were all uniform.


Probability Measure Compact Group Gauss Measure Compact Abelian Group Topological Semigroup 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Herbert Heyer
    • 1
  1. 1.Mathematisches InstitutUniversität TübingenTübingen 1Germany

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