A Besicovitch-Morse function preserving Lebesgue measure is constructed and shown to form a meager set among continuous measure-preserving maps.
Besicovitch, Discussion der stetigen Funktionen im Zusammenhang mit der Frage ¨ uber ihre Differentierbarkeit, Bulletin de l’Acad´ emie des Sciences de Russie, vol
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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.