Theorems · Theorem · measure theory
MeasureTheory.IntegrableAtFilter.eventually
∀ {α : Type u_1} {ε : Type u_3} {mα : MeasurableSpace α} {f : α → ε} {μ : MeasureTheory.Measure α}
[inst : TopologicalSpace ε] [inst_1 : ContinuousENorm ε] {l : Filter α},
MeasureTheory.IntegrableAtFilter f l μ → ∀ᶠ (s : Set α) in l.smallSets, MeasureTheory.IntegrableOn f s μ- Cited by
- 3 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Filterstatement and proof · cited by 8,121
- Filter.Eventuallystatement · cited by 3,134
- MeasureTheory.IntegrableOnstatement and proof · cited by 548
- ContinuousENormstatement and proof · cited by 290
- Filter.smallSetsstatement · cited by 89
- MeasureTheory.IntegrableAtFilterstatement and proof · cited by 66
- MeasureTheory.IntegrableOn.mono_setproof · cited by 60
- Filter.eventually_smallSets'proof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Asymptotics.IsBigO.integrableAtFilterproof · cited by 7
- Filter.Tendsto.integral_sub_linear_isLittleO_aeproof · cited by 3
- Filter.Tendsto.eventually_intervalIntegrable_aeproof · cited by 2