$L_{p}$ is:

- complete under the Lebesgue integral, this result is may be called the Riesz-Fischer theorem
- not complete under the Riemann integral: https://math.stackexchange.com/questions/397369/space-of-riemann-integrable-functions-not-complete

And then this is why quantum mechanics basically lives in $L_{2}$: 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

- Lebesgue integral | 31, 1k, 15
- Calculus | 17, 7k, 159
- Mathematics | 17, 13k, 336
- Ciro Santilli's Homepage | 262, 182k, 3k

- Complete metric space | 44
- Lebesgue integral vs Riemann integral | 201, 272, 1
- Lp space | 30, 408, 5