Let $a,b \in \mathbb{R}$ satisfy $a<b$, and let $f \in C([a,b];\mathbb{R})$. Let $\mathcal{B}([a,b])$ denote the Borel $\sigma$-algebra of $[a,b]$, and let $\lambda := \mathcal{L}^1\big|_{\mathcal{B}([a,b])}$ be the restriction of one-dimensional [Lebesgue measure](/page/Lebesgue%20Measure) to $([a,b],\mathcal{B}([a,b]))$. Then

\begin{align*} \|f\|_\infty = \|f\|_{L^\infty([a,b],\lambda)}. \end{align*}