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- TL;DR Summary
- I need a citation for the proposition that the only multivariate rotationally invariant distribution with iid components is a multivariate normal distribution.

I need a citation for the following proposition: Assume a random vector ##X=(X_1, ..., X_n)^T## with iid components ##X_i## and mean 0, then the distribution of ##X## is only invariant with respect to orthogonal transformations, if the distribution of the ##X_i## is a normal distribution.

Thank you for your help!

Thank you for your help!