Let F be a continuous injective map from an open subset of {Mathematical expression} to {Mathematical expression} . 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.
Denominator-preserving maps
PANTI, Giovanni
2012-01-01
Abstract
Let F be a continuous injective map from an open subset of {Mathematical expression} to {Mathematical expression} . 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.File in questo prodotto:
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