Lusin's condition \((N)\) for the space mappings \(W^{1,n}\) under analytic assumptions (Q1410440)

Let \(\Omega\) be a domain in \(\mathbb{R}^n\). A continuous mapping \(f: \Omega \mapsto \mathbb{R}^n\) is said to satisfy the Lusin condition if \(|f(A)|= 0\) for each \(A \subset \Omega\) such that \(|A|=0\) (where \(|A|\) is the Lebesgue measure of \(A\)). The paper deals with sufficient conditions ensuring that a continuous function \(f \in W^1_p (\Omega; \mathbb{R}^n)\) with the critical value \(p=n\) satisfies this Lusin condition.