4 problems

Let $\mathcal{W}^{\alpha,b}$ be the Banach space of $1$-periodic functions considered above. For a function $W_{\mathbf{t}}$ in this space, let … be the measure on its graph. For…

Uniform absorption conjecture. If $\boldsymbol{\mathcal{O}}$ is $w$-compact, then $\boldsymbol{\mathfrak{M}}$ is uniformly absorbing.

No-relaxation-gap conjecture. There is no relaxation gap between the trajectory formulation … , so that $p^*=P^*$.

Let $X$ be the state space and let $(\rho^k)$ be the sequence of discounted occupation-measure densities used in the paper's approximation scheme. The existing assumption requires…