Wilhelmus Anthonius Josephus Luxemburg ( Delft, 11 April 1929 – 2 October 2018) was a Dutch American mathematician who was a professor of mathematics at the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

. He received his B.A. from the

University of Leiden Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city of Le ...

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 The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. Luxemburg became a corresponding member of the Royal Netherlands Academy of Arts and Sciences in 1974. Luxemburg contributed to the development of

non-standard analysis The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta ...

by popularizing the construction of

hyperreal number In mathematics, the system of hyperreal numbers is a way of treating infinite and infinitesimal (infinitely small but non-zero) quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers ...

s in the 1960s. Though

Edwin Hewitt Edwin Hewitt (January 20, 1920, Everett, Washington – June 21, 1999) 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 z ...

had shown the construction in 1948, the formalization of non-standard analysis is generally associated with

Abraham Robinson Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorp ...

. Other notable work he did was in the theory of

Riesz space In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper ''Su ...

s (

partially ordered In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary r ...

vector space In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called '' vectors'', may be added together and multiplied ("scaled") by numbers called ''scalars''. Scalars are often real numbers, but can ...

s where the order structure is a

lattice Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an orna ...

).Caltech Mourns the Passing of Wilhelmus A. J. Luxemburg
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Selected publications

* 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 Holt McDougal is an American publishing company, a division of Houghton Mifflin Harcourt, that specializes in textbooks for use in high schools. The Holt name is derived from that of U.S. publisher Henry Holt (1840–1926), co-founder of the e ...

* 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 Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes referen ...

* 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 The University of Arkansas (U of A, UArk, or UA) is a public land-grant research university in Fayetteville, Arkansas. It is the flagship campus of the University of Arkansas System and the largest university in the state. Founded as Arkansas ...

, Fayetteville, Ark.

Selected publications

References

External links

See also