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Nonstandard Analysis for the Working Mathematician
Book by
- GenresMathematics
311 pages, Paperback
First published June 30, 2000
About the author
Peter A. Loeb
3 booksPeter Albert Loeb was a mathematician at the University of Illinois at Urbana–Champaign.
Loeb was born in Berkeley, California and studied at Reed College (1955-58) and Harvey Mudd College, where he obtained a B.S. in mathematics in 1959. He received his MS at Princeton University in 1961, and his PhD in mathematics from Stanford University in 1964 with a thesis supervised by Halsey Royden with a thesis titled An Axiomatic Treatment of Pairs of Elliptic Differential Equations.
He first became professor at the University of California, Los Angeles and in 1968 he took the position of assistant professor at the Mathematics Department of the University of Illinois where he remained for the rest of his career, from 1975 to 2008 as full professor and since then as professor emeritus.
Loeb's research covered a wide range of topics, mainly in potential theory, measure theory, functional analysis, and topology.
He co-authored a basic reference text on nonstandard analysis (Hurd–Loeb 1985). Reviewer Perry Smith for MathSciNet wrote:
This book is a welcome addition to the literature on nonstandard analysis.
The notion of Loeb measure named after him has become a standard tool in the field and is considered "likely to be his most enduring legacy".
Loeb supervised six PhD theses, among that of Sun Yeneng.
In 2012 Loeb became a fellow of the American Mathematical Society.
Loeb was born in Berkeley, California and studied at Reed College (1955-58) and Harvey Mudd College, where he obtained a B.S. in mathematics in 1959. He received his MS at Princeton University in 1961, and his PhD in mathematics from Stanford University in 1964 with a thesis supervised by Halsey Royden with a thesis titled An Axiomatic Treatment of Pairs of Elliptic Differential Equations.
He first became professor at the University of California, Los Angeles and in 1968 he took the position of assistant professor at the Mathematics Department of the University of Illinois where he remained for the rest of his career, from 1975 to 2008 as full professor and since then as professor emeritus.
Loeb's research covered a wide range of topics, mainly in potential theory, measure theory, functional analysis, and topology.
He co-authored a basic reference text on nonstandard analysis (Hurd–Loeb 1985). Reviewer Perry Smith for MathSciNet wrote:
This book is a welcome addition to the literature on nonstandard analysis.
The notion of Loeb measure named after him has become a standard tool in the field and is considered "likely to be his most enduring legacy".
Loeb supervised six PhD theses, among that of Sun Yeneng.
In 2012 Loeb became a fellow of the American Mathematical Society.
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