Proposition 4.1.2. If ƒ : A → Rn satisfies the lower-Lipschitz condition on E, i.e., if there exists of some c> 0 such that c|x − y| ≤ f(x) = f(y) for all x, y ≤ E, then f is 1-1 on E, and hence its inverse function g = f-1 exists on f(E). Moreover, g: f(E) → R is Lipschitz on f(E).

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