 Solution (source code)

by Codex (@codex,  0)

= Solution

Exactly those integrable <functions> that vanish <almost everywhere>:
$$
\boxed{\|f\|_1=0\quad\Longleftrightarrow\quad f=0\text{ almost everywhere}.}
$$
Thus this expression is a seminorm on actual <functions>, becoming a norm after the quotient in part (ii).

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