Show that for any measurable function $f$ in a measure space, we have:
$$
||f||_p \leq \max\{||f||_r ,||f||_s \}
$$
whenever $0<r<p<s$.
Now by splitting the integrals into parts where $f>1$ and $f\leq 1$, we could easily show that
$$
||f||_p \leq ||f||_r+||f||_s \
$$
But I have no idea how to show the stronger inequality as above.
2026-04-19 21:27:57.1776634077
$L^p$ spaces inclusion
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