Lineability in sequence and function spaces

We prove the existence of large algebraic structures-including large vector subspaces or infinitely generated free algebras-inside, among others, the family of Lebesgue measurable functions that are surjective in a strong sense, the family of nonconstant differentiable real functions vanishing on dense sets, and the family of discontinuous separately continuous real functions. Lineability in special spaces of sequences is also investigated.