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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.05169 |
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Table of Contents:
- We show that for any free probability measure-preserving action of $\mathbb{C}^{d}$ on a standard probability space, there exists a Borel entire function $F$ such that the factor map $x \mapsto F_{x}$, where $F_{x}(z) = F(z \cdot x)$, is injective. This work builds on a result of Glücksam and Weiss, who constructed non-constant measurable entire functions for such actions. The proof combines a separating cross-section whose cocycle values lie in a countable subgroup with Forstnerič's holomorphic approximation theorem with prescribed critical points.