Theorems · Theorem · measure theory
MeasureTheory.lintegral_coe_le_coe_iff_integral_le
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → NNReal},
MeasureTheory.Integrable (fun x => ↑(f x)) μ → ∀ {b : NNReal}, ∫⁻ (a : α), ↑(f a) ∂μ ≤ ↑b ↔ ∫ (a : α), ↑(f a) ∂μ ≤ ↑b- Cited by
- 1 results in Mathlib
- Foundations
- Depth 255 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.
- 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
- NNRealstatement and proof · cited by 4,310
- MeasureTheory.integralstatement and proof · cited by 1,779
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
- MeasureTheory.lintegralstatement · cited by 1,152
- ENNReal.coe_le_coeproof · cited by 73
- MeasureTheory.lintegral_coe_eq_integralproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_coe_le_of_lintegral_coe_leproof · cited by 1