In 1905 Henri Lebesgue [1905] published a large paper Sur les fonctions representables analytiquement, which strongly influenced the next investigations in a domain of mathematics that we call today the descriptive set theory. The paper was mainly devoted to the study of the Baire Hierarchy of real functions. Moreover, a proof of one theorem was wrong (the theorem is actually true). H. Lebesgue used the argument that a continuous image of a Borel set is a Borel set. M.J. Souslin [1917] observed the error and found a counterexample: a Borel set with a continuous image not being Borel. That was a beginning of the study of a new important class of subsets of the real line and Polish spaces.