Permutations and piecewise-constant approximation of continuous functions of n variables - Korneichuk, N. P. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We consider the problem of approximation of a continuous function f given on an n-dirnensional cube by step functions in the metrics of C and L p. We obtain exact error estimates in terms of the modulus of continuity of the function f or a special permutation of it.