Peter A. Loeb

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Peter Albert Loeb is a mathematician at the University of Illinois at Urbana–Champaign. He co-authored a basic reference text on non-standard 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[edit]


  1. ^ Perry Smith
  2. ^ Robert Goldblatt, Lectures on the hyperreals. An introduction to nonstandard analysis. Graduate Texts in Mathematics, 188. Springer-Verlag, New York, 1998.
  3. ^ List of Fellows of the American Mathematical Society, retrieved 2013-02-02.


  • 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[edit]

  • Peter Loeb, University of Illinois at Urbana-Champaign