Absolute convergence implies convergence in a Banach space ↩

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created: 2021-12-03 12:40:09
modified: 2022-01-10 04:13:04

is a Banach space.
Statement: Absolute convergence implies convergence in

.
That is, if:

Proof

This is easy to see from the fact that

So is a vector in with finite length, so the series converge.