4 problems

Let $Q=(q_n)_{n\geq 1}$ be a dynamically generated basic sequence, and let $\mathcal{UN}(Q)$ denote the set of uniformly $Q$-normal numbers. Uniform normality multiplication conjec…

Let $Q=(q_n)_{n\geq 1}$ be a nondeterministic dynamically generated basic sequence. Let $\mathcal{N}(Q)$, $\mathcal{DN}(Q)$, and $\mathcal{UN}(Q)$ denote the corresponding normalit…

Let $Q=(q_n)_{n\geq 1}$ be a deterministic dynamically generated basic sequence. Write $\mathcal{N}(Q)$ for the set of $Q$-normal numbers, $\mathcal{UN}(Q)$ for the uniformly $Q$-n…

Let $Q=(q_n)_{n\geq 1}$ be a deterministic dynamically generated basic sequence. Let the strongest hotspot theorem refer to the assertion that the hotspot hypotheses imply membersh…