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:
, for x y
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..