Incoming links: Complete metric space
is:
- complete under the Lebesgue integral, this result is may be called the Riesz-Fischer theorem
- not complete under the Riemann integral: math.stackexchange.com/questions/397369/space-of-riemann-integrable-functions-not-complete
And then this is why quantum mechanics basically lives in : not being complete makes no sense physically, it would mean that you can get closer and closer to states that don't exist!
TODO intuition