5 problems

Let $f\colon\mathbb{N}\to\mathbb{R}$ be a tempered function, let $(X,\mathscr{B},\mu,T)$ be an invertible probability measure-preserving system, let $k\in\mathbb{N}$, let…

Weighted fifth-order central limit conjecture. There exists such a weighting function $\bar w$ and a universal constant $C_3>0$ for which

Let $w^*(x)\in C_0^\infty([0,1])$ be a weighting function used in a weighted Birkhoff average, and let $N$ denote the number of samples. The preceding result gives a nearly linear-…

Let $\mathcal{H}$ be a Hardy field, let $f_1,\ldots,f_k,W\in\mathcal{H}$, and define … Property (WP) is that, for every $f\in\operatorname{span}^*(f_1,\ldots,f_k)$ and…

Positive-measure divergence conjecture. There exists a sequence of probability measures $\{\mu_n\}$ such that