[Q.] Is there a semicontinuous function, which has its discontinuous set with non-zero measure?
Remark: Given a semicontinuous function, the set of all discontinuous points may be uncountable, for instance, an indicator function on a Cantor set.
I also found a paper here with its title: "Baire order of functions are continuous almost everywhere", see this link:
I do not understand this paper, but does it say all semicontinuous functions are continuous almost everywhere, since it is baire-1 function?