Department Mathematik



Mathematisches Kolloquium

Am Freitag, 10. November 2006, um 15:30 Uhr spricht

Prof. Dr. Peter A. Loeb
(University of Illinois at Urbana-Champaign)

im Hörsaal E27 über das Thema

Applications of rich measure spaces formed from nonstandard models

Zusammenfassung: In 1960, Abraham Robinson constructed an ordered field extension of the real numbers that contained infinitely large and infinitely small numbers. His construction allows one to rigorously treat the calculus with the use of infinitesimals, and much more. The existence, for example, of infinitely large natural numbers means that certain infinite sets have the combinatorial properties of finite sets. In 1975, the speaker showed that such sets support a rich, new measure structure that has since been used by Horst Osswald and many other to treat a broad spectrum of problems in pure and applied mathematics. The recent work of Yeneng Sun shows that this structure finally gives a rigorous foundation for the treatment of a continuum of independent random variables and to the corresponding applications in mathematical economics. After discussing this background the talk presents a recent application by Yeneng Sun and the speaker to purification of measure-valued maps and the extension of results eliminating randomness in game-theoretic settings.
Alle Interessierten sind hiermit herzlich eingeladen.
Im Anschluß an die Veranstaltung, ab 19:00 Uhr gemeinsames Abendessen im Ratskeller am Marienplatz