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On coincidence of Pettis and McShane integrability

Marián J. Fabián — 2015

Czechoslovak Mathematical Journal

R. Deville and J. Rodríguez 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...

Remarks on continuous images of Radon-Nikodým compacta

Marián J. FabiánMartin HeislerEva Matoušková — 1998

Commentationes Mathematicae Universitatis Carolinae

A family of compact spaces containing continuous images of Radon-Nikod’ym compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikod’ym compact K we prove: If K is totally disconnected, then it is Radon-Nikod’ym compact. If K is adequate, then it is even Eberlein compact.

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