A note on singularity of a recently introduced family of Minkowski's question-mark functions

摘要

AbstractWe point out a mistake in the proof of the main theorem in a recent article on a family of generalized Minkowski's question-mark functions, saying that each member of the family is a singular homeomorphism, and provide two alternative proofs, one based on the ergodicity of the Gauss mapGand theα-Lüroth mapLα, and another one focusing more on classical properties of continued fraction expansions.]]>