Spaceability and algebrability of sets of nowhere integrable functions (Q2838959)

If \(X\) is a topological vector space and \(S\subset X\) then \(S\) and \(X\) is said to be lineable, spaceable, if \(S\cup\{0\}\) contains and infinite dimensional, closed infinite dimensional, vector subspace of \(X\). Among the many results of this paper we mention the following. The set of continuous but not absolutely continuous functions on \([0,1]\) is a lineable subset of the space of Kurzweil integrable functions that are not Lebesgue integrable, and that this latter set is spaceable in the space of all Kurzweil integrable functions. The authors also show that there is an infinite dimensional vector space of differentiable functions \(S\) such that every element of the closure, in the continuity norm, of \(S\) is a Kurzweil integrable function.