Additive properties of certain classes of pathological functions (Q2510975)

In this note the author deals with certain additive properties of the following three classes of functions acting from \(\mathbb{R}\) into itself: a) Continuous nowhere differentiable functions; b) Sierpiński-Zygmund functions, i.e., those functions whose restrictions to all subsets of \(\mathbb{R}\) of cardinality continuum are discontinuous; c) Absolutely nonmeasurable functions, i.e., those functions which are nonmeasurable with respect to all nonzero \(\sigma\)-finite continuous measures on \(\mathbb{R}\). Some results are derived assuming Martin's axiom or the continuum hypothesis.