Search results for "universal integrability"

MR2569913: Rodríguez, José. Some examples in vector integration. Bull. Aust. Math. Soc. 80 (2009), no. 3, 384–392. (Reviewer: Luisa Di Piazza),

2009

The paper deals with some classical examples in vector integration due to Phillips, Hagler and Talagrand, revisited from the point of view of the Birkhoff and McShane integrals. More precisely, the author considers: - Phillips' example of a Pettis integrable function f which is not Birkhoff integrable [R. S. Phillips, Trans. Amer. Math. Soc. 47 (1940), 114--145; MR0002707 (2,103c)]. It is proved here that f is universally McShane integrable. - Hagler's example of a scalarly measurable l∞-valued function g which is not strongly measurable. The function g is proved to be universally Birkhoff integrable. - Talagrand's example of a bounded Pettis integrable function φ having no conditional expe…