An absolutely continuous function whose inverse functionis not absolutely continuous


Abstract


We construct a strictly increasing function f:[0,1] \to [0,1] such that f(0)=1,f is absolutely continuous, and f^-1 is not absolutely continuous. Functions of this type are very scarce in the literature.

DOI Code: 10.1285/i15900932v23n1p47

Keywords: Absolutely continuous functions; Cantor functions

Classification: 26A46; 26A30

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