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  • POLAR DECOMPOSITION OF THE k-FOLD PRODUCT OF LEBESGUE MEASURE ON ℝn

  • Part of
  • S. REZA MOGHADASI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 85 / Issue 2 / April 2012
    Published online by Cambridge University Press:
    06 January 2012, pp. 315-324
    Print publication:
    April 2012
    • Article
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  • The Blaschke–Petkantschin formula is a geometric measure decomposition of the q-fold product of Lebesgue measure on ℝn. Here we discuss another decomposition called polar decomposition by considering ℝn×⋯×ℝn as ℳn×k and using its polar decomposition. This is a generalisation of the Blaschke–Petkantschin formula and may be useful when one needs to integrate a function g:ℝn×⋯×ℝn→ℝ with rotational symmetry, that is, for each orthogonal transformation O,g(O(x1),…,O(xk))=g(x1,…xk). As an application we compute the moments of a Gaussian determinant.