I've been told before that if $g$ is random over $V$, then the reals of $V$ have full outer measure in $V[g]$ (and are therefore nonmeasurable). Is there a good reference/easy proof for this fact?
2026-03-30 06:43:05.1774852985
Random forcing preserves outer measure
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See Lemma 2.15 in Brendle's lecture notes:
https://www.math.uni-hamburg.de/personen/khomskii/ST2013/bogotalecture.pdf