【学术报告】2018年8月7日上午吕凡副教授来我院举办学术讲座

2018-08-06 16:43:40    浏览次数:

\begin{equation*}

E(0, \varphi)=\{\beta>1\colon |T^{n}_{\beta}1-0|<\varphi(n) \textrm{ for infinitely many } n\in\mathbb{N}\}

\end{equation*}

is of zero or full Lebesgue measure in $(1,+\infty)$ according to $\sum\varphi(n)<+\infty$ or not, where $T_{\beta}$ is the $\beta$-transformation. We also determine the Lebesgue measure of the following set

\begin{equation*}

\mathfrak{E}(0, \{l_{n}\})=\{\beta>1\colon |T^{n}_{\beta}1-0|<\beta^{-l_{n}} \text{ for infinitely many } n\in\mathbb{N}\}.

\end{equation*}