 Descriptive set theory (DST) is the study of certain kinds of definable sets of real numbers, which are obtained from simple kinds (like the open sets and the closed sets) by well-understood operations like complementation or projection. The Borel sets were the first hierarchy of definable sets, introduced in the 1898 book of Émile Borel; they are obtained from the open sets by iterated application of the operations of countable union and complementation. In 1905 Lebesgue studied the Borel sets in an epochal memoir, showing that their hierarchy has levels for all countable ordinals, and analyzing the Baire functions as counterparts of the Borel sets. The main aim of descriptive set theory is to find structural properties common to all such definable sets: for instance, the Borel sets were shown to have the perfect set property (if uncountable, they have a perfect subset) and thus to comply with the continuum hypothesis (CH). This result was established in 1916 by Hausdorff and by Alexandroff, working independently. Other important “regularity properties” studied in DST are the property of being Lebesgue measurable, and the so-called property of Baire (to differ from an open set by a so-called meager set, or set of first category).