Lebesgue points of functions in complex Sobolev spaces

The complex Sobolev space was introduced by Dinh and Sibony in complex dynamics. We show that the complement of the set of Lebesgue points for functions in complex Sobolev spaces is pluripolar. This in particular says that there is a canonical representation of functions in the complex Sobolev spaces. This is a joint-work with Gabriel Vigny.