EN
Let 1 ≤ p < ∞, k ≥ 1, and let Ω ⊂ ℝⁿ be an arbitrary open set. We prove a converse of the Calderón-Zygmund theorem that a function $f ∈ W^{k,p}(Ω)$ possesses an $L^{p}$ derivative of order k at almost every point x ∈ Ω and obtain a characterization of the space $W^{k,p}(Ω)$. Our method is based on distributional arguments and a pointwise inequality due to Bojarski and Hajłasz.