Let $f=g$ pointwise a.e. in $\mathbb{R}$. Then what can we say about the Lebesgue points of $f$ and $g$?
Clearly the set of Lebesgue points of $f$ (denoted by $L_f$)and that of $g$ (denoted by $L_g$)need not equal. Is there any relation between these two sets?
Can we expect something like $\mu(L_f) \cap \mu(L_g)=\mu(L_f)=\mu(L_g)$?
P.S.: Answers with a clean proof / a precise reference are greatly appreciated.