Mazur–Orlicz theorem and asymptotic formula for the error in supreme norm

We prove Mazur–Orlicz theorem in supreme norm, cf. Mazur and Orlicz, Sur quelques propriétés des fonctions periodiques, Studia Math. 9 (1940) 1–16 using ergodic theory. We use it in the calculation of asymptotic formula for the error in cardinal interpolation and in shift invariant operators.