Theorems · Theorem · measure theory
MeasureTheory.integrable_count_iff
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} [inst : NormedAddCommGroup β] [MeasurableSingletonClass α]
{f : α → β}, MeasureTheory.Integrable f MeasureTheory.Measure.count ↔ Summable fun x => ‖f x‖A function is integrable for the counting measure iff its norm is summable.
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- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- NormedAddCommGroupstatement and proof · cited by 15,752
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- Set.univproof · cited by 3,945
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- BorelSpaceproof · cited by 1,602
- MeasureTheory.Integrablestatement · cited by 1,367
- Summablestatement and proof · cited by 778
- MeasureTheory.AEStronglyMeasurableproof · cited by 755
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