- 2005 年 2 月 9 日（水曜日）16:00〜17:00
- Dr. Pedro Teran （Zaragoza(スペイン)大学）
- Aumann and Herer expectations: solution of an open problem in stochastic geometry
- Among the several existing definitions of the expectation (or integral) of a
random set, there are those given by Aumann in the 60's and by Herer in the
90's. While the former needs a Banach space structure, the latter makes sense
in a metric space. It is known that Aumann's expectation is always a subset of
Herer's, and that the converse holds in Hilbert spaces.
The problem to prove whether both expectations are the same generally, or
otherwise to characterize the Banach spaces where they actually are, is thus
significant and was posed by Prof. Ilya Molchanov in 1996.
I will answer that question and explain some related results. For the sake of
suspense, the solution is not given here.
- 〒840-8502 佐賀市本庄町1 佐賀大学理工学部数理科学科
TEL 0952-28-8522 FAX 0952-28-8501
Any questions, comments, suggestions and so on are welcome. Please