[wfunction]

> But consider another example where the underlying target was "all points with rational coordinates". All the probes in a grid sampling scheme would hit the target, but the target has measure zero.

And how exactly would the Monte Carlo version differ here? Every single random number generated is going to be rational isn't it?

[robzyb]

Every single random number being generated will be rational, but that is much finer granularity than any fixed grid that you might be using.

Unless your fixed grid includes every single rational point that could be expressed by the (P)RNG.