3 ms·
Won’t the reals we can construct by any computation be enumerable? What measure can they have if not zero?
by dullcrisp 1y ago
Won’t the reals we can construct by any computation be enumerable? What measure can they have if not zero?
- andrewla 1y agoYes, they have measure zero. So the question becomes whether "measure" is a useful concept at all. In my opinion, no, it is not. It's just another artifact of non-constructive and meaningless abstractions. Many modern courses in analysis skip measure theory except as a historical artifact because the gauge integral is more powerful than the Lebesgue integral and doesn't require leaving the bounds of sanity to get there.