Certainly! Probability 0 does not mean impossible.

In this case it does. Describe any effective measure to pick a random sample from the interval and you will have cheated into choosing from the computable reals instead (of which there is a countable amount)

	▲	fc417fc802 5 hours ago \| parent \| next [-]
		I don't think that's correct. You're describing a limitation of our physical computing devices (or perhaps physical reality itself) as opposed to a theoretical flaw. At least as far as I can tell.
	▲	LPisGood 5 hours ago \| parent \| prev [-]
		Measure 0 is different than empty.