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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

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