Why would this property mean that it is “bigger”? You can construct a uniform distribution of a uncountable set through a probability density as well. However, using the same measure on a countably infinite subset of the uncountable set would show that the countable set has measure 0.
Or a counterexample from the other direction would be that you can’t describe a uniform distribution of the empty set either (I think). And that would feel even weirder to call “bigger”.
Why would this property mean that it is “bigger”? You can construct a uniform distribution of a uncountable set through a probability density as well. However, using the same measure on a countably infinite subset of the uncountable set would show that the countable set has measure 0.
Or a counterexample from the other direction would be that you can’t describe a uniform distribution of the empty set either (I think). And that would feel even weirder to call “bigger”.