Theorems · Theorem · measure theory
MeasureTheory.ofReal_toReal_ae_eq
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal},
(∀ᵐ (x : α) ∂μ, f x < ⊤) → (fun x => ENNReal.ofReal (f x).toReal) =ᵐ[μ] f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 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.
- 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.EventuallyEqstatement · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- LT.lt.neproof · cited by 872
- ENNReal.ofRealstatement · cited by 863
- ENNReal.toRealstatement · cited by 859
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_toRealproof · cited by 15
- MeasureTheory.pdf.ofReal_toReal_ae_eqproof · cited by 1