$$
\begin{array}{l}
A=\left\{1,10, \frac{1}{10}\right\}, \\
B=\{y \mid y=\lg x, x \in A\} .
\end{array}
$$

Then $A \cap B=$
$-1 .\{1\}$.

From the problem, we know
$$
\begin{aligned}
B & =\left\{y \mid y=\lg 1, y=\lg 10, y=\lg \frac{1}{10}\right\} \\
& =\{0,1,-1\} .
\end{aligned}
$$

Therefore, $A \cap B=\{1\}$.