论文标题
Bernoulli随机性和有偏见的正态性
Bernoulli Randomness and Biased Normality
论文作者
论文摘要
可以考虑$ 2^ω$上的概率度量$μ$的$μ$ -martin-löf随机性，例如bernoulli量度$μ_p$给定$ p \ in（0，1）$。我们研究了$ n^ω$的bernoulli随机性，带有参数$ p_0，p_1，\ dotsc，p_ {n-1} $，我们引入了一个偏见的正态性。我们证明，每个Bernoulli随机真实的真实是在有偏见的意义上都是正常的，这具有推论，即有偏见的正常实物的集合具有$ n^ω$的完整bernoulli度量。我们给出了一种用于从正常序列计算偏见的正常序列的算法，以便我们可以提供明确的正常现实实例。我们研究了随机性对迭代功能系统的应用。最后，我们列出了与Bernoulli随机性和偏见正常性有关的其他一些问题。
One can consider $μ$-Martin-Löf randomness for a probability measure $μ$ on $2^ω$, such as the Bernoulli measure $μ_p$ given $p \in (0, 1)$. We study Bernoulli randomness of sequences in $n^ω$ with parameters $p_0, p_1, \dotsc, p_{n-1}$, and we introduce a biased version of normality. We prove that every Bernoulli random real is normal in the biased sense, and this has the corollary that the set of biased normal reals has full Bernoulli measure in $n^ω$. We give an algorithm for computing biased normal sequences from normal sequences, so that we can give explicit examples of biased normal reals. We investigate an application of randomness to iterated function systems. Finally, we list a few further questions relating to Bernoulli randomness and biased normality.
