Hello,

I'm looking for a theorem that states that under certain coditions (which? I'm flexible.), the expected value of a function that works on vectors, will be the same for all orthogonal vectors.

Namely, given a function

( or , doesn't matter to me ) ,

and under certain conditions, this holds:

, forxy

Is there anything that even remotely suggests this kind of thing?

(I'm talking about large n values, of\course.)

I know this sounds like a statistics problem, I just figured there's more chance that discrete math \ set theory people would use this kind of theorem..