I am familiar with infinite sets. As for measure, the entire QS argument is about the proportion of your measure in favourable scenarios. If you have a good argument as to why total measure does not matter but proportion of measure does, I'd love to hear it. Make sure that the answer is consistent with your implied view that total measure does matter on finite sets.
I don't have a very good argument for either side, which is why I am not discounting one or the other.
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