Working on an exercise from Shorack's Probability for Statisticians, Ex 3.4.3 (Littlewood's inequality). Can't seem to find any material for this. Help is appreciated.
Prove:Exercise 4.3 (Littlewood's inequality) Let $m_r \equiv \mathbb{E}|X|^r$ denote the $r$th absolute moment. Then for $r \ge s \ge t \ge 0$, we have $m^{r-s}_t m^{s-t}_r \ge m^{r-t}_s$.
Thank you very much!