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Emile Borel’s Set Theory

Frank J. Swetz (The Pennsylvania State University)

Émile Borel (1871–1956), a student of Gaston Darboux (1842–1917), formulated the concept of a measurable set in 1894, resulting in the positing of the Heine-Borel Theorem. His work employed nested intervals on the real number line, helped define the concept of compactness, and extended the notion of integrability. The text on set theory shown above, Élements de la Théorie des Ensembles, was published in 1949 and was one of his last works.

In Chapter 5 of Ensembles, Borel discussed his work on measurability.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in Mathematical Treasures. In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Frank J. Swetz (The Pennsylvania State University), "Emile Borel’s Set Theory," Loci (May 2014)