Wilhelmus Luxemburg

Wilhelmus Anthonius Josephus Luxemburg is Professor of Mathematics, Emeritus 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.

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.

Selected publications

• 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.

See also

• Influence of non-standard analysis