In reply to Rick Wicklin.

Thanks for answering, even though the thread is two-and-a-half years old!

Ad. 2: What does 'measure zero' mean? I'm decent at using math, but not that familiar with thinking about math. Maybe I'm thinking too analytically here, but is this basically the question on whether or not the borders of an area are included within that area or not? Same actually with the < resp. =< from your point 3.

Ad. 3: Given the nature of Monte Carlo and random numbers, I understand your point. Though, analytically again, in the limit for infinite points, I think there could still be a difference.