Theorems · Theorem · measure theory
MeasureTheory.hasFiniteIntegral_const_iff_enorm
∀ {α : Type u_1} {ε : Type u_4} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : ENorm ε] {c : ε},
‖c‖ₑ ≠ ⊤ → (MeasureTheory.HasFiniteIntegral (fun x => c) μ ↔ ‖c‖ₑ = 0 ∨ MeasureTheory.IsFiniteMeasure μ)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ENorm
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Set.univproof · cited by 3,945
- MeasureTheory.IsFiniteMeasurestatement · cited by 1,078
- ENorm.enormstatement and proof · cited by 715
- ENormstatement and proof · cited by 155
- MeasureTheory.lintegral_constproof · cited by 123
- MeasureTheory.HasFiniteIntegralstatement · cited by 120
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.integrable_const_iff_enormproof · cited by 5
- MeasureTheory.hasFiniteIntegral_const_enormproof · cited by 2
- MeasureTheory.hasFiniteIntegral_const_iffproof · cited by 1
- MeasureTheory.hasFiniteIntegral_const_iff_isFiniteMeasure_enormproof · cited by 1