We study the set $\mathrm{\Gamma }$ consisting of univoque sequences, the set $\mathrm{\Lambda }$ consisting of sequences in which the lengths of consecutive zeros and consecutive ones are bounded, and their frequency subsets ${\mathrm{\Gamma }}_a$, ${\underset{\_}{\mathrm{\Gamma }}}_a$, ${\overline{\mathrm{\Gamma }}}_a$ and ${\mathrm{\Lambda }}_a$, ${\underset{\_}{\mathrm{\Lambda }}}_a$, ${\overline{\mathrm{\Lambda }}}_a$ consisting of sequences respectively in $\mathrm{\Gamma }$ and $\mathrm{\Lambda }$ with frequency, lower frequency and upper frequency of zeros equal to some $a\in [0,1]$. The Hausdorff dimension of all these sets are obtained by studying the dynamical system $({\mathrm{\Lambda }}^{\left(m\right)},\sigma )$ where $\sigma$ is the shift map and ${\mathrm{\Lambda }}^{\left(m\right)}=\left\{w\in \{0,1{\}}^{\mathbb{N}}:w\mathrm{d}\mathrm{o}\mathrm{e}\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{t}\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{i}\mathrm{n}{0}^m\mathrm{o}\mathrm{r}{1}^m\right\}$ for integer $m\ge 3$, studying the Bernoulli-type measures on ${\mathrm{\Lambda }}^{\left(m\right)}$ and finding out the unique equivalent $\sigma$-invariant ergodic probability measure.

我们研究集合 $\mathrm{\Gamma }$ 由唯一序列组成，集合 $\mathrm{\Lambda }$ 由连续 0 和连续 1 的长度有界的序列及其频率子集组成 ${\mathrm{\Gamma }}_{\mathrm{一种}}$, ${\underset{\_}{\mathrm{\Gamma }}}_{\mathrm{一种}}$, ${\overline{\mathrm{\Gamma }}}_{\mathrm{一种}}$ 和 ${\mathrm{\Lambda }}_{\mathrm{一种}}$, ${\underset{\_}{\mathrm{\Lambda }}}_{\mathrm{一种}}$, ${\overline{\mathrm{\Lambda }}}_{\mathrm{一种}}$ 分别由序列组成 $\mathrm{\Gamma }$ 和 $\mathrm{\Lambda }$ 频率、低频和零的高频等于一些 $\mathrm{一种}\in [0,1]$. 所有这些集合的豪斯多夫维数都是通过研究动力系统获得的$({\mathrm{\Lambda }}^{\left(米\right)},\sigma )$ 在哪里 $\sigma$ 是移位映射和 ${\mathrm{\Lambda }}^{\left(米\right)}=\left\{瓦\in \{0,1{\}}^{\mathbb{N}}：瓦\mathrm{d}\mathrm{Ø}\mathrm{电子}\mathrm{秒}\mathrm{n}\mathrm{Ø}\mathrm{吨}\mathrm{C}\mathrm{Ø}\mathrm{n}\mathrm{吨}\mathrm{一种}\mathrm{一世}\mathrm{n}{0}^{米}\mathrm{Ø}\mathrm{r}{1}^{米}\right\}$ 对于整数 $米\ge 3$, 研究伯努利型测度 ${\mathrm{\Lambda }}^{\left(米\right)}$ 并找出唯一的等价物 $\sigma$-不变遍历概率测度。