> If that's true, then there can be no measure satisfying the requirements even when weakened from countable additivity to finite additivity.
I think this is an important/interesting point and should be highlighted more in the article. The "magic trick" is not hidden in the fact that you are using infinitely many pieces. The "magic trick" is that the pieces have very odd shapes.
I think this is an important/interesting point and should be highlighted more in the article. The "magic trick" is not hidden in the fact that you are using infinitely many pieces. The "magic trick" is that the pieces have very odd shapes.