Silver Measurability and its relation to other regularity properties

For $a\subs b\subs\omega$ with $b{\setminus} a$ infinite, the set $D\,{=}\,\{x\in\reals\,{:}\, a\subs x\subs b\}$ is called a doughnut. Doughnuts are equivalent to conditions of Silver forcing, and so, a set $S\subs\reals$ is called Silver measurable, or completely doughnut, if for every doughnut $D$ there is a doughnut $D'\subs D$ which is contained in or disjoint from $S$. In this paper, we investigate the Silver measurability of $\bDelta$ and $\bSigma$ sets of reals and compare it to other regularity properties like the Baire and the Ramsey property and Miller and Sacks measurability.