How can I prove that nested sequence of non-empty bounded closed convex sets in Hilbert space have nonempty intersection?
I just don't know where to start.
Thanks
How can I prove that nested sequence of non-empty bounded closed convex sets in Hilbert space have nonempty intersection?
I just don't know where to start.
Thanks
This is Cantors Intersection Theorem. The (simple) proof can be found here for example. You need to use the fact that closed bounded convex subsets in a Hilbert space H are weakly compact.