An absolutely continuous function whose inverse functionis not absolutely continuous


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

Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.