Luzin's (N) and randomness reflection

@article{Pauly2020LuzinsA,
  title={Luzin's (N) and randomness reflection},
  author={A. Pauly and L. Westrick and Liang Yu},
  journal={arXiv: Logic},
  year={2020}
}
We show that a computable function $f:\mathbb R\rightarrow\mathbb R$ has Luzin's property (N) if and only if it reflects $\Delta^1_1(\mathcal O)$-randomness, and if and only if it reflects $\mathcal O$-Kurtz randomness, but reflecting Martin-Lof randomness or weak-2-randomness does not suffice. Here a function $f$ is said to reflect a randomness notion $R$ if whenever $f(x)$ is $R$-random, then $x$ is $R$-random as well. If additionally $f$ is known to have bounded variation, then we show $f… Expand

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