I was wondering relations of $L_p$ spaces..
Let $E$ be a measurable set. If $E$ is of finite measure, then $L_p(E) \subset L_q(E)$, $1 \le p \le q \le \infty$.
However, does it still hold if $E$ is infinite?
I was wondering relations of $L_p$ spaces..
Let $E$ be a measurable set. If $E$ is of finite measure, then $L_p(E) \subset L_q(E)$, $1 \le p \le q \le \infty$.
However, does it still hold if $E$ is infinite?