Yes, but in a countable measure space the measure is determined entirely by the measures on the points, hence there is no problem with making the interpretation “probability 0 = impossible”, and this sort of weirdness does not occur.
Countability is not precisely the condition needed to avoid this, but it’s certainly a sufficient condition.
Yes, but in a countable measure space the measure is determined entirely by the measures on the points, hence there is no problem with making the interpretation “probability 0 = impossible”, and this sort of weirdness does not occur.
Countability is not precisely the condition needed to avoid this, but it’s certainly a sufficient condition.
Uh, what sort of weirdness does not occur?