A note on gaussian distributions in R^n

Published 8 Aug 2011 in math.ST and stat.TH | (1108.1647v3)

Abstract: Given any finite set F of (n - 1)-dimensional subspaces of Rⁿ we give examples of nongaussian probability measures in Rⁿ whose marginal distribution in each subspace from F is gaussian. However, if F is an infinite family of such (n - 1)-dimensional subspaces then such a nongaussian probability measure in Rⁿ does not exist.

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