Geodesic
Lineability Issues Involving Vector-Valued Measurable and Integrable Functions
Journal of convex analysis, Tome 19 (2012) no. 2, pp. 393-402
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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.
Mots-clés : Strongly measurable, scalarly measurable, omega-star-scalarly measurable, McShane integrable functions, Bochner integrable functions 
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     author = {F. J. Garc{\'\i}a-Pacheco and M. A. Sofi},
     title = {Lineability {Issues} {Involving} {Vector-Valued} {Measurable} and {Integrable} {Functions}},
     journal = {Journal of convex analysis},
     pages = {393--402},
     year = {2012},
     volume = {19},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_2_JCA_2012_19_2_a4/}
}
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F. J. García-Pacheco; M. A. Sofi. Lineability Issues Involving Vector-Valued Measurable and Integrable Functions. Journal of convex analysis, Tome 19 (2012) no. 2, pp. 393-402. http://geodesic.mathdoc.fr/item/JCA_2012_19_2_JCA_2012_19_2_a4/