Theorems · Theorem · measure theory
MeasureTheory.hasFiniteIntegral_toReal_iff
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal},
(∀ᵐ (x : α) ∂μ, f x ≠ ⊤) → (MeasureTheory.HasFiniteIntegral (fun x => (f x).toReal) μ ↔ ∫⁻ (x : α), f x ∂μ ≠ ⊤)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- ENNReal.ofRealproof · cited by 863
- ENNReal.toRealstatement and proof · cited by 859
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.integrable_toReal_iffproof · cited by 1