Solution
= Solution
The <Lipschitz continuity> of $p_1$ gives
$$
|e_1(x)-p_1(x)|
\leq\frac CL\sum_{\ell=1}^L
\lVert X_{(\ell)}-x\rVert_\infty
\leq C\lVert X_{(L)}-x\rVert_\infty.
$$
Part (d) therefore implies
$$
\boxed{\mathbb E|e_1(x)-p_1(x)|
\leq C\left\{
\left(\frac{2L}{nM}\right)^{1/d}+\frac2L
\right\}.}
$$