Solution (source code)

= Solution

For $1\leq p<\infty$, $L^p(E,\mathcal E,\mu)$ consists of <measurable functions> with $\int_E|f|^p\,d\mu<\infty$, identifying functions equal <almost everywhere>. Its <Lp norm> is $\|f\|_p=(\int|f|^p)^{1/p}$. Thus membership is a condition on an almost-everywhere <equivalence class>, not on individual point values.