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

作者:Fernandez Sanchez Juan; Trutschnig Wolfgang
来源:Comptes Rendus Mathematique, 2017, 355(9): 956-959.
DOI:10.1016/j.crma.2017.09.009

摘要

We 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 map G and the alpha-Luroth map L-alpha, and another one focusing more on classical properties of continued fraction expansions.

  • 出版日期2017-9

全文