Given a measure space $(\Omega,\mathfrak A,\mu)$ and $1≤q≤p$, how can I show that $$L_p(\mu)\subseteq L_q(\mu)$$ if the measure $\mu$ is finite, that means $\mu(\Omega)<\infty$?
2026-04-26 10:17:20.1777198640
$L_p(\mu)\subseteq L_q(\mu)$
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Hint:
$$|f(x)|^q \le \max(|f(x)|^p,1)$$