On coincidence of Pettis and McShane integrability

0443124 - MÚ 2016 RIV CZ eng J - Článek v odborném periodiku
Fabian, Marián
On coincidence of Pettis and McShane integrability.
Czechoslovak Mathematical Journal. Roč. 65, č. 1 (2015), s. 83-106. ISSN 0011-4642. E-ISSN 1572-9141
Grant CEP: GA ČR(CZ) GAP201/12/0290
Institucionální podpora: RVO:67985840
Klíčová slova: Pettis integral * McShane integral * MC-filling family
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.284, rok: 2015
http://link.springer.com/article/10.1007/s10587-015-0161-x

R. Deville and J. Rodriguez proved that, for every Hilbert generated space X, every Pettis integrable function f[0,1]X is McShane integrable. R. Avilés, G. Plebanek, and J. Rodríguez constructed a weakly compactly generated Banach space X and a scalarly null (hence Pettis integrable) function from [0,1] into X, which was not McShane integrable. We study here the mechanism behind the McShane integrability of scalarly negligible functions from [0,1] (mostly) into C(K) spaces. We focus in more detail on the behavior of several concrete Eberlein (Corson) compact spaces K, that are not uniform Eberlein, with respect to the integrability of some natural scalarly negligible functions from [0,1] into C(K) in McShane sense.
Trvalý link: http://hdl.handle.net/11104/0245880