Any free pmp action of C^d admits a Borel entire function F such that the factor map x ↦ F_x(z) = F(z · x) is injective.
A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas
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Separating Orbits by Entire Functions
Any free pmp action of C^d admits a Borel entire function F such that the factor map x ↦ F_x(z) = F(z · x) is injective.