The moral intuition that we should use the continuous/​Lebesgue measure here seems tied up with the intuition that consciousness is continuous and not a bunch of instantanenous frames with gaps between them. If it is in fact instantaneous with gaps, then the moral intuition seems unreliable and you should probably go with the counting measure instead, with which the frames would have nonzero measure.
FWIW, I’m not a moral realist, and if it turned out both kinds of beings were possible together, then there could be no fact of the matter about how to weigh them against each other. But maybe I’d want to weight the continuous minds infinitely more anyway. You could use the continuous measure first, and then break ties with the counting measure.
The moral intuition that we should use the continuous/​Lebesgue measure here seems tied up with the intuition that consciousness is continuous and not a bunch of instantanenous frames with gaps between them. If it is in fact instantaneous with gaps, then the moral intuition seems unreliable and you should probably go with the counting measure instead, with which the frames would have nonzero measure.
FWIW, I’m not a moral realist, and if it turned out both kinds of beings were possible together, then there could be no fact of the matter about how to weigh them against each other. But maybe I’d want to weight the continuous minds infinitely more anyway. You could use the continuous measure first, and then break ties with the counting measure.