2 problems

Let $G$ be a countable amenable group. An IP$^{*}$-set in $G$ is a set meeting the image of every increasing IP sequence, where an increasing IP sequence is a map…

Let $G=B_1\cup\dotsm\cup B_q$ be a finite partition of a semimodule $(G,\pmb{+})$ over a semiring $(R,+,\cdot)$. For a subset $F\subseteq R$, write $Fb=\{fb:f\in F\}$. Schur–Brauer…