A Besicovitch-Morse function preserving Lebesgue measure is constructed and shown to form a meager set among continuous measure-preserving maps.
Bobok, On non-differentiable measure-preserving functions , Real Analysis Exchange 16(1)(1991), 119-129
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A Besicovitch-Morse function preserving the Lebesgue measure
A Besicovitch-Morse function preserving Lebesgue measure is constructed and shown to form a meager set among continuous measure-preserving maps.