In Folland’s Real Analysis book, we have the following proposition:
“ If $\mu(X)< \infty$ and $0<p<q\le \infty$, then $L^p(\mu)\supset L^q(\mu)$.”
So suppose that $A$ is a finite set and $\mu$ is the counting measure on $A$. If $0<p<q\le\infty$, does it follow that $\mathscr l^p(A)\supset \mathscr l^q(A)$? I am asking this question because usually I see the reverse inclusion for $\mathscr l^p$ spaces.