Gaussian Measures as Limits on Irreducible Symmetric Spaces and Cones
نویسنده
چکیده
We prove central limit theorems of Lindeberg-L evy and Lindeberg-Feller type for any K-invariant random variables on all irreducible symmetric spaces and irreducible symmetric cones, completing in this way the numerous partial results known before. In all cases the limit measures turn out to be Gaussian and being such a limit characterizes these measures. On the other hand we show that other classical characterizations of Gaussian measures on R n , like 2-stability and the Bernstein theorem, are not true on symmetric spaces.
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