[asdkashdkjashd]

You have to assume that the one-dimensional marginals are Gaussian for otherwise the statement is not correct.

[darkmighty]

Hmm I'm not sure I get your point. I'm trying to prove that the joint pdf of N iid RV's is isotropic if and only if the RV's are gaussian. If I assume the pdfs are gaussian in the first place the proof isn't valid?

[asdkashdkjashd]

Oh, I see. I thought you were trying to prove something different.