A note on gaussian distributions in Rⁿ

2011/08/08 by B.G. Manjunath, K. R. Parthasarathy, Manjunath, B. G. +1
Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Statistics Theory (math.ST) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1108.1647

openalex publication_date 2011/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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