Theorems · Theorem · measure theory
intervalIntegral.abs_integral_mono_interval
∀ {f : ℝ → ℝ} {a b : ℝ} {μ : MeasureTheory.Measure ℝ} {c d : ℝ},
Set.uIoc a b ⊆ Set.uIoc c d →
0 ≤ᵐ[μ.restrict (Set.uIoc c d)] f →
IntervalIntegrable f μ c d → |∫ (x : ℝ) in a..b, f x ∂μ| ≤ |∫ (x : ℝ) in c..d, f x ∂μ|- Cited by
- 0 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.ofPredproof · cited by 6,101
- MeasureTheory.aestatement and proof · cited by 2,352
- absstatement · cited by 1,814
- MeasureTheory.integralproof · cited by 1,779
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- le_rflproof · cited by 1,558
- intervalIntegralstatement · cited by 546
- Filter.EventuallyLEstatement and proof · cited by 383
- IntervalIntegrablestatement and proof · cited by 316
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