On the Fubini theorem for the Pettis integral for bounded functions

• Autorzy: Michalak A.
• Języki publikacji: EN

Abstrakty

EN

We show that if X is a WGG Banach space and it does not contain any isomorphic copy of l1, then for every bounded Pettis integrable function f : [0, 1]^2 --> X* there exists a scalarly equivalent function for which the Fubini theorem for the Pettis integral holds. On the other hand, we show that for every bounded Pettis integrable function f : [0, 1]^2 --> l^2 (R) there exists a scalarly equivalent bounded function for which the Fubini theorem for the Pettis integral does not hold. We also show (assuming the Martin axiom) that there exists a bounded Pettis integrable function f : [0, 1]^2 --> L^[infinity](lambda) such that for each function g scalarly equivalent to f the function s --> g(t, s) is not weakly measurable for almost every t [belongs to] [0, 1].

Słowa kluczowe

EN

Fubini theorem; Pettis integral; translations on compact groups

PL

całka Pettisa; translacja na grupach zwartych; twierdzenie Fubiniego

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 1
• Strony: 1--14
• Opis fizyczny: Bibliogr. 16 poz.,

Twórcy

autor

Michalak A.

• Faculty of Mathematics and Computer Sciences, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland,