Let $N \in \mathbb{N} \cup \{0\}$, let $x_0,\dots,x_N \in [-1,1]$ be distinct interpolation nodes, and let $\mathcal{P}_N$ denote the real [vector space](/page/Vector%20Space) of polynomials of degree at most $N$ restricted to $[-1,1]$. For each $j \in \{0,\dots,N\}$, let $\ell_j \in \mathcal{P}_N$ be the Lagrange basis polynomial determined by $\ell_j(x_i)=\delta_{ij}$. Define the interpolation operator

\begin{align*} I_N: C([-1,1]) \to \mathcal{P}_N \end{align*}

by $(I_N f)(x_j)=f(x_j)$ for every $j \in \{0,\dots,N\}$, and define the Lebesgue constant

\begin{align*} \lambda_N := \max_{x \in [-1,1]} \sum_{j=0}^N |\ell_j(x)|. \end{align*}

Then, for every $f \in C([-1,1])$,

\begin{align*} \|f-I_N f\|_\infty \leq (1+\lambda_N)\inf_{p\in\mathcal P_N}\|f-p\|_\infty. \end{align*}