[ultrafilter]

Theorems 1 and 3 are finitary and easier to physically interpret. As for Theorem 2, "With probably p a random foo has property bar" intends no interpretation of "random foo"; it merely claims that the set of foo's with property bar has measure p with respect to some probability measure. In this case, the probability measure is the Bernoulli measure.

http://www.encyclopediaofmath.org/index.php/Bernoulli_measur...