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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. Luxemburg became a corresponding member of the Royal Netherlands Academy of Arts and Sciences in 1974.
Joseph Dauben (1995) attributes the ultrapower construction of the hyperreal numbers to Luxemburg in 1962. Such a construction was originally introduced by Edwin Hewitt in 1948, and popularized by Luxemburg in the 1960s.
- Luxemburg, W. A. J.; Zaanen, A. C. (1971) Riesz spaces. Vol. I. North-Holland Mathematical Library. North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., New York.
- Luxemburg, Wilhelmus Anthonius Josephus (1955) Banach function spaces. Thesis, Technische Hogeschool te Delft, 1955.
- Stroyan, K. D.; Luxemburg, W. A. J. (1976) Introduction to the theory of infinitesimals. Pure and Applied Mathematics, No. 72. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London.
- Luxemburg, W. A. J. (1969) A general theory of monads. 1969 Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) pp. 18–86 Holt, Rinehart and Winston, New York.
- Luxemburg, W. A. J.; Schep, A. R. (1978) A Radon-Nikodym type theorem for positive operators and a dual. Nederl. Akad. Wetensch. Indag. Math. 40, no. 3, 357—375.
- Luxemburg, W. A. J. (1979) Some aspects of the theory of Riesz spaces. University of Arkansas Lecture Notes in Mathematics, 4. University of Arkansas, Fayetteville, Ark.
- 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, N.J.: Princeton University Press, 1995).