4. For a function $f(x)$ defined on the interval $[a, b]$, if there exists a constant $c$, such that for any $x_{1} \in[a, b]$ there is a unique $x_{2} \in[a, b]$, satisfying $\frac{f\left(x_{1}\right)+f\left(x_{2}\right)}{2}=c$, then the function $f(x)$ is said to have a "mean" of $c$ on $[a, b]$. Then, the mean of the function $f(x)=\lg x$ on $[10,100]$ is ( ).
(A) 10
(B) $\frac{1}{10}$
(C) $\frac{3}{2}$
(D) $\frac{3}{4}$
4. C.

Let for any $x_{1} \in [10,100]$, there exists a unique $x_{2} \in$ $[10,100]$, such that $x_{1} x_{2}=10^{3}$. Therefore,
$$
\begin{array}{l}
\frac{f\left(x_{1}\right)+f\left(x_{2}\right)}{2}=\frac{\lg x_{1}+\lg x_{2}}{2} \\
=\frac{\lg x_{1} x_{2}}{2}=\frac{\lg 10^{3}}{2}=\frac{3}{2} .
\end{array}
$$