Journal of Convex Analysis 19 (2012), No. 2, 393--402
Copyright Heldermann Verlag 2012
Lineability Issues Involving Vector-Valued Measurable and Integrable Functions
Francisco J. García-Pacheco
Dept. of Mathematics, University of Cadiz, 11510 Puerto Real, Spain
garcia.pacheco@uca.es
Mohd Amin Sofi
Dept. of Mathematics, Kashmir University, Srinagar-190006 (J&K), India
aminsofi@rediffmail.com
We construct, over many Banach spaces, infinite dimensional vector spaces of scalarly measurable functions that are not strongly measurable, and infinite dimensional vector spaces of ω*-scalarly measurable functions that are not scalarly measurable. A similar result will be proved for the set of McShane-integrable functions which are not Bochner-integrable.
Keywords: Strongly measurable, scalarly measurable, omega-star-scalarly measurable, McShane integrable functions, Bochner integrable functions.
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