论文标题
卢赞（N）和随机反射
Luzin's (N) and randomness reflection
论文作者
论文摘要
We show that a computable function $f:\mathbb R\rightarrow\mathbb R$ has Luzin's property (N) if and only if it reflects $Π^1_1$-randomnes, if and only if it reflects $Δ^1_1(\mathcal O)$-randomness, and if and only if it reflects $\mathcal O$-Kurtz randomness, but reflecting Martin-Löf随机性或弱2随机不足。在这里，如果$ f（x）$是$ r $ -random，则可以反映一个随机性概念$ r $，而$ x $也是$ r $ random。如果众所周知，$ f $具有有限的变化，那么我们显示$ f $具有luzin（n）时，并且仅当它反映feal-2随机性时，并且当且仅当它反映$ \ emptyset的$ - kurtz kurtz随机性时。这将经典的真实分析与算法随机性联系起来。
We show that a computable function $f:\mathbb R\rightarrow\mathbb R$ has Luzin's property (N) if and only if it reflects $Π^1_1$-randomnes, if and only if it reflects $Δ^1_1(\mathcal O)$-randomness, and if and only if it reflects $\mathcal O$-Kurtz randomness, but reflecting Martin-Löf 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 $f$ has Luzin's (N) if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset'$-Kurtz randomness. This links classical real analysis with algorithmic randomness.
