Peter Albert Loeb (born July 3, 1937) is a mathematician at the
University of Illinois at Urbana–Champaign
The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Unive ...
. He co-authored a basic reference text on
nonstandard 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–delt ...
(Hurd–Loeb 1985). Reviewer Perry Smith for
MathSciNet
MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal '' Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links ...
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.
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 ...
.
List of Fellows of the American Mathematical Society
retrieved 2013-02-02.
See also
*Influence of nonstandard analysis Abraham Robinson's theory of nonstandard analysis has been applied in a number of fields.
Probability theory
"Radically elementary probability theory" of Edward Nelson combines the discrete and the continuous theory through the infinitesimal appr ...
Notes
Publications
*Hurd, Albert E.; Loeb, Peter A. ''An introduction to nonstandard real analysis''. Pure and Applied Mathematics, 118. Academic Press, Inc., Orlando, FL, 1985.
*Loeb, Peter A. "Conversion from nonstandard to standard measure spaces and applications in probability theory". ''Trans. Amer. Math. Soc.'' 211 (1975), 113–122.
*Loeb, Peter A. "A new proof of the Tychonoff theorem". ''American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America.
The ''American Mathematical Monthly'' is an ...
'' 72 1965 711–717.
*Bliedtner, J.; Loeb, P. "A reduction technique for limit theorems in analysis and probability theory". Ark. Mat. 30 (1992), no. 1, 25–43.
*Loeb, Peter A. "Weak limits of measures and the standard part map". ''Proceedings of the American Mathematical Society'' 77 (1979), no. 1, 128–135.
*Füredi, Zoltán; Loeb, Peter A. "On the best constant for the Besicovitch covering theorem". ''Proc. Amer. Math. Soc.'' 121 (1994), no. 4, 1063–1073.
*Loeb, Peter A. "A nonstandard functional approach to Fubini's theorem". ''Proc. Amer. Math.'' Soc. 93 (1985), no. 2, 343–346.
*Loeb, Peter; Sun, Yeneng: "Purification of measure-valued maps". ''Illinois Journal of Mathematics'' 50 (2006), no. 1-4, 747–762.
*Loeb, Peter A.; Osswald, Horst "Nonstandard integration theory in topological vector lattices". Monatsch. Math. 124 (1997), no. 1, 53–82.
*Loeb, Peter A. "An axiomatic treatment of pairs of elliptic differential equations". ''Annales de l'Institut Fourier'' (Grenoble) 16 1966 fasc. 2, 167–208.
External links
Peter Loeb
University of Illinois at Urbana-Champaign
{{DEFAULTSORT:Loeb, Peter A.
Mathematical logicians
Living people
University of Illinois Urbana-Champaign faculty
Fellows of the American Mathematical Society
1937 births
People from Berkeley, California