Let \((X,\mcm,m)\) be a measure space and let \(f\colon X\to\CC\) be measurable. The \(L^\infty\) norm of \(f\) is \[ \norm{f}_\infty \coloneqq \inf \theset{\alpha \geq 0 \suchthat m\qty{\theset{x\in X\suchthat \abs{f(x)} \geq \alpha}} = 0} \in[0,\infty]. \]
When \(\norm{f}_\infty<\infty\), it is the least real number \(c\) with \(\abs{f}\leq c\) almost everywhere.
What is the infinity norm $\norm{f}_\infty$?