X is r.v. on ($\Omega$,F,P) where $E[\left\lvert X \right\rvert^a] < \infty$. Prove $E[\left\lvert X \right\rvert^b] < \infty$ for all $0<b\le a$
Suppose $\mu(X)<\infty$. Show that if $\ f\in\ L^q(X,\mu)$ for some $1\le q<\infty$ then $\ f\in\ L^r(X,\mu)$ for $1\le r<q$