I am working on a project about how the universal cover of a connected Lie group is a Lie group, but I cannot find a theorem that assures that this universal cover actually exists. I've found references on:
Lie Groups, An Approach through Invariants and Representations, by Claudio Procesi: page 80.
Probability on Compact Lie Groups by David Applebaum: page 5.
But I have not found the actual statement nor proof of the result anywhere. Does anybody know where I may find it?