Lebesgue integral of is complete but Riemann isn't
ID: lebesgue-integral-of-lp-is-complete-but-riemann-isn-t
Lebesgue integral of is complete but Riemann isn't by 
Ciro Santilli 37 Updated 2025-05-29 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-29 +Created 1970-01-01 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!
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