On Lusin’s condition for the inverse function. (English) Zbl 0562.26002

The following theorem is proved. Let \(U\subset R^ n\) be open and \(\phi:U\to R^ n\) be continuous and one-to-one. If \(\phi\) is differentiable almost everywhere on U, then the inverse \(\phi^{-1}\) satisfies the Lusin’s condition (N) if and only if the Jacobian \(J_{\phi}\neq 0\) almost everywhere on U. Some known corollaries for the functions \(f:<a,b>\to R\) are added.
Reviewer: A.Neubrunnová


26B05 Continuity and differentiation questions
26B10 Implicit function theorems, Jacobians, transformations with several variables
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