# Denominator-preserving maps

@article{Panti2011DenominatorpreservingM, title={Denominator-preserving maps}, author={Giovanni Panti}, journal={Aequationes mathematicae}, year={2011}, volume={84}, pages={13-25} }

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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