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**Wilhelmus Anthonius Josephus Luxemburg** (11 April 1929 – 2 October 2018)^{[1]}^{[2]} was a Dutch American mathematician who was a professor of mathematics at the California Institute of Technology.

He received his B.A. from the University of Leiden in 1950; his M.A., in 1953; his Ph.D., from the Delft Institute of Technology, in 1955. He was assistant professor at Caltech during 1958–60; Associate Professor, during 1960–62; Professor, during 1962–2000; Professor Emeritus, from 2000. He was the Executive Officer for Mathematics during 1970–85. In 2012 he became a fellow of the American Mathematical Society.^{[3]} Luxemburg became a corresponding member of the Royal Netherlands Academy of Arts and Sciences in 1974.^{[4]}

Luxemburg contributed to the development of non-standard analysis by popularizing the construction of hyperreal numbers in the 1960s. Though Edwin Hewitt had shown the construction in 1948, the formalization of non-standard analysis is generally associated with Abraham Robinson.^{[5]}

Other notable work he did was in the theory of Riesz spaces (partially ordered vector spaces where the order structure is a lattice).^{[6]}

- 1955:
*Banach function spaces*. Thesis, Technische Hogeschool te Delft, 1955. - 1969: "A general theory of monads", in
*Applications of Model Theory to Algebra, Analysis, and Probability*(Internat. Sympos., Pasadena, Calif., 1967) pp. 18–86 Holt, Rinehart and Winston - 1971: (with Zaanen, A. C.)
*Riesz Spaces*. Vol. I. North-Holland Mathematical Library. North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., New York. - 1976: (with Stroyan, K. D.)
*Introduction to the Theory of Infinitesimals*. Pure and Applied Mathematics, No. 72. Academic Press - 1978: (with Schep, A. R.) "A Radon-Nikodym type theorem for positive operators and a dual", Nederl. Akad. Wetensch. Indag. Math. 40, no. 3, 357–375.
- 1979:
*Some Aspects of the Theory of Riesz Spaces*, University of Arkansas Lecture Notes in Mathematics, 4. University of Arkansas, Fayetteville, Ark.

**^**"Caltech Mourns the Passing of Wilhelmus A. J. Luxemburg". Archived from the original on 2018-10-03. Retrieved 2018-10-03.**^**American Men and Women of Science (2004), Thomson Gale**^**List of Fellows of the American Mathematical Society, retrieved 2013-02-02.**^**"W.A.J. Luxemburg". Royal Netherlands Academy of Arts and Sciences. Archived from the original on 8 February 2016. Retrieved 8 February 2016.**^**Joseph Dauben (1995)*Abraham Robinson: The Creation of Nonstandard Analysis: A Personal and Mathematical Odyssey*, Princeton University Press**^**"Caltech Mourns the Passing of Wilhelmus A. J. Luxemburg". Archived from the original on 2018-10-03. Retrieved 2018-10-03.

- Wilhelmus Luxemburg at the Mathematics Genealogy Project