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Introduction and brief survey
Invariant measures on manifolds
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a n x k matrix assume Borel measure Borel subsets canonical change of variable Chapter coefficient compact sets compact subset complex numbers compute correlation countable covariance matrix decomposition diagonal entries diagonal matrix differential forms discussed eigenvalues elements equations Example exists factors finite follows Fourier transform GL(k GL(n globally defined group algebra Haar measure hence Hint homogeneous polynomial idempotents identity independently distributed integral invariant Haar measure invariant measure inverse James Laplace transform Lebesgue measure Lemma locally compact Math maximal invariant n x n noncentral Chi-square nonsingular nonzero normal density function notation obtain open set orthogonal matrix parameter partition permutation polynomial of degree probability density function Proof random variables rank real numbers result row space satisfies Section Show Statist Suppose symmetric matrix theory tion topology uniquely determined variance vector Wishart density zonal polynomials