Continuity of Measure

January 31, 2024

My friend Rohan recently posed a problem to me: can you think of a collection of sets $A_k$ such that the finite intersections $\bigcap_{k=1}^n A_k$ are nonempty for all integers $n$, but the infinite intersection $\bigcap_{k=1}^\infty A_k$ is empty?

Anyway, it reminded me of this neat idea in measure theory, so I wrote him a brief summary and figured I should put it here too.

Continuity of Measure (PDF)