Modifications of sequence selection principles

We study modifications of the sequence selection principles for real functions obtained by allowing other than continuous functions and/or by replacing the pointwise convergence by quasi-normal or discrete convergence. We show that for important families of real functions we obtain already known sequence selection principles. Replacing the pointwise convergence we obtain plenty of sequence selection principles and we try to find equivalences or implications among them. Finally we attempt to show that these modifications are useful tools for proofs of known results or their strengthening.