In this second lecture on the topic of weak convergence that we are showing, Melanie discusses key properties of weakly convergent sequences in Banach and Hilbert spaces, including Mazur’s Theorem that ensures that if we pass to a weak limit in a closed convex set then the resulting limit must also be in the set.

You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists):    • Oxford Mathematics Student Lectures -...  

All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.