Shcherbina’s theorem for finely holomorphic functions

We prove an analogue of Sadullaev's theorem concerning the size of the set where a maximal totally real manifold M can meet a pluripolar set. M has to be of class C-1 only. This readily leads to a version of Shcherbina's theorem for C-1 functions f that are defined in a neighborhood of certain compact sets K subset of C. If the graph Gamma(f) (K) is pluripolar, then. partial derivative f/partial derivative z = 0 in the closure of the fine interior of K.