Let fi, i = 1, ..., n, be copies of a random variable f and let N be an Orlicz function. We show that for every x ∈ ℝn the expectation E∥(xifi)i=1n∥N is maximal (up to an absolute constant) if fi, i = 1, ..., n, are independent. In that case we show that the expectation E∥(xi fi)i=1n∥ N is equivalent to ∥x∥M, for some Orlicz function M depending on N and on distribution of f only. We provide applications of this result.
- Orlicz norms
- Random variables