Theoretical Statistics and Mathematics Unit, ISI Delhi

A note on Gaussian distributions in $\mathbb{R}^n$

by B. G. Manjunath and K. R. Parthasarathy

Given any finite set $\mathcal{F}$ of $(n-1)$-- dimensional subspaces of $\mathbb{R}^n$ we give
examples of nongaussian probability measures in $\mathbb{R}^n$ whose marginal distribution in each subspace from
$\mathcal{F}$ is gaussian. However, if $\mathcal{F}$ is an infinite family of such $(n-1)$--dimensional subspaces then
such a nongaussian probability measure in $\mathbb{R}^n$ does not exist.

isid/ms/2011/16 [fulltext]

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