 Lusin summarized the state of the art in his 1930 book Leçons sur les ensembles analytiques (Paris, Gauthier-Villars), which was to be a key reference for years to come. Since this work, it has become customary to present results in DST for the Baire space \( ^{\omega}\)\(\omega\) of infinite sequences of natural numbers, which in effect had been introduced by René Baire in a paper published in 1909. Baire space is endowed with a certain topology that makes it homeomorphic to the set of the irrational numbers, and it is regarded by experts to be “perhaps the most fundamental object of study of set theory” next to the set of natural numbers [Moschovakis 1994, 135].