A note on Gaussian distributions in ℝn

Given any finite set of ( n  − 1)-dimensional subspaces of ℝ n we give examples of nonGaussian probability measures in ℝ n whose marginal distribution in each subspace from is Gaussian. However, if is an infinite family of such ( n  − 1)-dimensional subspaces then such a nonGaussian probability meas...

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Bibliographic Details
Published in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2012, Vol.122 (4), p.635-644
Main Authors: MANJUNATH, B G, PARTHASARATHY, K R
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Summary:Given any finite set of ( n  − 1)-dimensional subspaces of ℝ n we give examples of nonGaussian probability measures in ℝ n whose marginal distribution in each subspace from is Gaussian. However, if is an infinite family of such ( n  − 1)-dimensional subspaces then such a nonGaussian probability measure in ℝ n does not exist.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-012-0099-y