I have to show the inclusion $L^{p}(\mathbb{Z},\mu) \subset L^{q}(\mathbb{Z},\mu)$ with the counting measure. Using 1≤p<q≤$\infty$ and the definition of the $L^{p}/L^{q}$ spaces I have tried to mess around with Hölder's inequality and the integral in the given space (which is just summation) to somehow show the inclusion for a given function but have been unsuccesful until now.
2026-03-27 23:35:30.1774654530
For 1≤p<q≤$\infty$, show that $L^{p}(\mathbb{Z},\mu) \subset L^{q}(\mathbb{Z},\mu)$, $\mu$ being the counting measure.
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