Peter A. Loeb Explained

Peter Albert Loeb (born July 3, 1937) is a mathematician at the University of Illinois at Urbana–Champaign. 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.^[1] The notion of Loeb measure named after him has become a standard tool in the field.^[2]

In 2012 he became a fellow of the American Mathematical Society.^[3]

See also

• Influence of nonstandard analysis

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 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

Notes and References

1. https://www.ams.org/mathscinet-getitem?mr=806135 Perry Smith
2. [Robert Goldblatt]
3. https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society