Theorems · Theorem · measure theory
MeasureTheory.hasFiniteIntegral_count_iff
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} [inst : NormedAddCommGroup β] [MeasurableSingletonClass α]
{f : α → β}, MeasureTheory.HasFiniteIntegral f MeasureTheory.Measure.count ↔ Summable fun x => ‖f x‖A function has finite integral for the counting measure iff its norm is summable.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- Top.topproof · cited by 9,680
- Norm.normstatement and proof · cited by 5,413
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- ENNReal.ofNNRealproof · cited by 1,279
- NNNorm.nnnormproof · cited by 952
- Summablestatement and proof · cited by 778
- MeasurableSingletonClassstatement and proof · cited by 230
- MeasureTheory.HasFiniteIntegralstatement · cited by 120
- MeasureTheory.Measure.countstatement · cited by 60
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.integrable_count_iffproof · cited by 0