Solution
= Solution
At a Lebesgue point, $f*g_n(x)-f(x)=\int g(u)[f(x-u/n)-f(x)]du$. Compact support and boundedness of $g$ reduce this to a constant times the mean oscillation over a ball of radius $O(1/n)$, which tends to zero.
= Solution
At a Lebesgue point, $f*g_n(x)-f(x)=\int g(u)[f(x-u/n)-f(x)]du$. Compact support and boundedness of $g$ reduce this to a constant times the mean oscillation over a ball of radius $O(1/n)$, which tends to zero.