It is well-known that if $V[G]$ is a generic extension by adding a Cohen real, then the set $\{r \in V[G]: r$ is Cohen generic over $V\}$ has measure zero.

On the other hand, if $V[G]$ is a generic extension by adding a random real, then the set $\{r \in V[G]: r$ is random over $V\}$ has outer measure one.

Question.I am wondering what is know about other generic reals? Are there any cases where the answer for them is not known?

Please provide references or proofs for each case.

everyreal in $S = \mathbb R^{V[g]} \setminus \mathbb R^V$ is a Sacks real, so if $S$ were null then $S \cup (S+g)$ would be too; however, $S \cup (S+g) = \mathbb R^{V[g]}$. Because $S$ is closed under rational translations, its being non-null implies it has full outer measure. My guess would be that $\mathbb R^V$ is null in $V[g]$, but I'm not sure right now. $\endgroup$ – Will Brian Dec 13 '18 at 21:44