Denominator-preserving maps

@article{Panti2011DenominatorpreservingM,
  title={Denominator-preserving maps},
  author={Giovanni Panti},
  journal={Aequationes mathematicae},
  year={2011},
  volume={84},
  pages={13-25}
}
  • Giovanni Panti
  • Published 2011
  • Mathematics
  • Aequationes mathematicae
  • Let F be a continuous injective map from an open subset of $${\mathbb {R}^n}$$ to $${\mathbb {R}^n}$$ . Assume that, for infinitely many k ≥ 1, F induces a bijection between the rational points of denominator k in the domain and those in the image (the denominator of (a1/b1, . . . , an/bn) being the l.c.m. of b1, . . . , bn). Then F preserves the Lebesgue measure. 

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