Theorems · Theorem · measure theory
MeasureTheory.setIntegral_nonneg_of_ae
∀ {X : Type u_1} {mX : MeasurableSpace X} {μ : MeasureTheory.Measure X} {f : X → ℝ} {s : Set X},
0 ≤ᵐ[μ] f → 0 ≤ ∫ (x : X) in s, f x ∂μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- Filter.EventuallyLEstatement and proof · cited by 383
- MeasureTheory.ae_restrict_of_aeproof · cited by 46
- MeasureTheory.setIntegral_nonneg_of_ae_restrictproof · cited by 5
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