Denominator-preserving maps
Abstract
Let F be a continuous injective map from an open subset of Rn to Rn. 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.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.