The following problem was raised by Nishino and remained open for more than 40 years:

Let f be a continuous map from the unit disc to complex plane such that its graph G(f) is a pluripolar set in C^2. Does it follow that f is holomorphic?

The main purpose of these two lectures is to give a solution to this problem (which was published in Acta Mathematica). In the first lecture we discuss all the preparatory statements and start with the proof of our theorem.