2 problems

Let $W=(W_1,W_2,\ldots)$ have a thinning-invariant gap distribution, let $T_1,T_2,\ldots$ be independent exponential random variables of mean one, and let $M$ be the almost-surely…

Let $\mathscr{K}'$ be the disjoint union of $\mathcal{M}_{+,1}(\mathbb{R})\times(0,\infty)$ and $0$, and let $\mathcal{M}_{\mathrm{st}}(\mathscr{K}')$ denote measures invariant und…