5 problems

Transducer measurability conjecture. There is a $\sigma$-algebra on $I \mathrel{\triangleright} O$ that, among other things, would allow one to define maps in the other direction,…

Let $\mathcal{P}(\mathbb{R})$ denote the finitely supported probability measures on $\mathbb{R}$, and let a support-preserving endomorphism be an endomorphism of this space that pr…

Let $p$ be prime, $k\geq1$, $G=\mathbb{F}_p^n$, and $\mathbb D=\{z\in\mathbb C:|z|\leq1\}$. Let $\varepsilon:\mathbb N\to\mathbb R^+$ be decreasing, and let $\mathrm{Poly}^k(G)$ be…

Measurability-removal conjecture. The $w^*$-scalar measurability assumption on $\partial\varphi(\bar{x},\cdot)$ imposed in Theorem 2 and satisfied in separable Asplund spaces can b…

Brian–Mislove conjecture. This technique always produces a non-Haar-measurable subgroup of $G$.