Let such that and let be measurable subsets of . Suppose that for each point , there are at least sets in that contain . Prove that there exists such that .
Let such that and let be measurable subsets of . Suppose that for each point , there are at least sets in that contain . Prove that there exists such that .
Here's the basic idea. Suppose that then , but why is that stupid (hint: use the idea that rougly the 's ' -fold cover' ).