Solution
= Solution
For $1\leq p<\infty$, the <Lp norm> is $\|f\|_p=(\int_E|f|^p\,d\mu)^{1/p}$; for $p=\infty$ it is the <essential supremum> of $|f|$. The <Lp space> consists of measurable functions with finite <norm>, identifying functions equal almost everywhere. This identification makes the quantity a <norm> rather than only a seminorm. \b[Convergence in $L^p$ means $\|f_n-f\|_p\to0$], including the essential-supremum <norm> when $p=\infty$.