Wilhelmus Luxemburg
Encyclopedia
Wilhelmus 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.
Joseph Dauben
(1995) attributes the ultrapower construction of the hyperreal number
s to Luxemburg in 1962. Such a construction was originally introduced by Edwin Hewitt
in 1948, and popularized by Luxemburg in the 1960s.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, 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.
Joseph Dauben
Joseph Dauben
Joseph W. Dauben is a Herbert H. Lehman Distinguished Professor of History at the Graduate Center of the City University of New York. He obtained his Ph.D...
(1995) attributes the ultrapower construction of the hyperreal number
Hyperreal number
The system of hyperreal numbers represents a rigorous method of treating the infinite and infinitesimal quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form1 + 1 + \cdots + 1. \, Such a number is...
s to Luxemburg in 1962. Such a construction was originally introduced by Edwin Hewitt
Edwin Hewitt
Edwin Hewitt was an American mathematician known for his work in abstract harmonic analysis and for his discovery, in collaboration with Leonard Jimmie Savage, of the Hewitt–Savage zero-one law.He received his Ph.D...
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.Keith StroyanKeith D. Stroyan is Professor of Mathematics at the University of Iowa. His main research interests are in analysis and visual depth perception.-Publications:...
; 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-Nikodֳ½m 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.