A simple proof for the upper bound of a theorem of T. Łuczak
Lei Shang, Lulu Fang · Colloquium Mathematicum · 2024
Let $b,c \gt 1$, and let $[a_1(x),a_2(x),a_3(x),\ldots ]$ be the continued fraction expansion of $x\in [0,1)$. The Hausdorff dimensions of the sets $$ \widetilde E(b,c)=\{x\in [0,1): a_n(x) \geq c^{b^n}\ \text{for all}\ n \in \mathbb N\} $$ and $$ E(b,c)=