 In the period 1900–1930, the rubric “set theory” was still understood to include topics in topology and the theory of functions. Although Cantor, Dedekind, and Zermelo had left that stage behind to concentrate on pure set theory, for mathematicians at large this would still take a long time. Thus, at the first International Congress of Mathematicians, 1897, keynote speeches given by Hadamard and Hurwitz defended set theory on the basis of its importance for analysis. Around 1900, motivated by topics in analysis, important work was done by three French experts: Borel [1898], Baire [1899] and Lebesgue [1902] [1905]. Their work inaugurated the development of descriptive set theory by extending Cantor’s studies on definable sets of real numbers (in which he had established that the Continuum Hypothesis is valid for closed sets). They introduced the hierarchy of Borel sets, the Baire hierarchy of functions, and the concept of Lebesgue measure—a crucial concept of modern analysis.