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Oct 12, 2015 at 4:18 comment added Noah Schweber Thank you very much for this answer! I've accepted, and asked a new question expanding on the rest of this question: mathoverflow.net/questions/220687/….
Oct 12, 2015 at 3:47 vote accept Noah Schweber
Sep 27, 2015 at 1:34 comment added Noah Schweber Something I missed at first glance, which I'm mentioning here because it might be interesting to others: this argument is essentially the same as the proof that if Empty has a winning strategy in the perfect set game for $X$, then $X$ is countable.
Sep 26, 2015 at 23:36 comment added Noah Schweber This is very nice! It doesn't obviously extend to the continuously strong measure zero case, though, does it? The natural game to play in that case would be: player I plays epsilons, player II plays intervals, but is allowed to pass. But in that game, many reals can be killed at a given stage, so the analysis seems to break down. Or am I missing something?
Sep 26, 2015 at 9:53 history answered Andreas Blass CC BY-SA 3.0