Lineability and unbounded, continuous and integrable functions

We investigate the existence of algebraic structures in the set of continuous, unbounded and integrable functions in [ 0,∞) , continuing the work initiated by Calderón-Moreno et al. (J. Math. Anal. Appl. 470:348-359, 2019). We explore the stricter notions of ( α ,β) -lineability/spaceability and pointwise lineability/spaceability, which were recently introduced. For example, we prove that the aforementioned set is pointwise spaceable, in particular, spaceable. On the other hand, negative results are also obtained. For instance, we prove the non ( ℵ _0,𝔠) -spaceability of the family of unbounded, continuous and integrable functions.