Lineability Issues Involving Vector-Valued Measurable and Integrable Functions

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 $\omega^*$-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.