4 problems

Let $X$ be the Markov process on $[0,1]$ and let $Y$ be the Markov process on $\mathbb{Z}_{\geq 0}$ with generator … Let $B([0,1]\times\mathbb{Z}_{\geq 0})$ be the Banach space of…

Let $T$ be the integration functional underlying the spaces $L^p(T)$ and $L^q(T)$, let $p\in(1,\infty)$, and let $q$ be its conjugate exponent, so that $1/p+1/q=1$. Denote the $T$-…

Let $\langle X,\tau,\mathbf{B}\rangle$ be an $\mathcal{S}$-Priestley space. For subsets $U,V\subseteq X$, write $V^{c}=X\setminus V$ and let $\downarrow W$ denote the down-set gene…

Let $\langle X,\tau,\mathbf{B}\rangle$ be an $\mathcal{S}$-Priestley space, and let $X_{B}$ denote the subset associated with $\mathbf{B}$ in the Priestley duality. The clopen up-s…