4 ms·
You first split the sphere into an uncountable number of subsets, then group these into a finite number of subsets, whose measure sum to twice the measure of th
by emblaegh 2y ago
You first split the sphere into an uncountable number of subsets, then group these into a finite number of subsets, whose measure sum to twice the measure of the original set.
(Un)countability is at the core of most of the counterintuitive results of measure theory, exactly because of the the third property of measure.
- adroniser 2y agoTo be clear, the construction given here violates the finite additivity property of measure. It's got nothing to do with the countable/uncountable additivity property.