Theorems · Theorem · measure theory
MeasureTheory.Measure.setIntegral_toReal_rnDeriv_le
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [MeasureTheory.SigmaFinite μ] {s : Set α},
μ s ≠ ⊤ → ∫ (x : α) in s, (μ.rnDeriv ν x).toReal ∂ν ≤ μ.real s- Cited by
- 0 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.SigmaFinite
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Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- MeasurableSetproof · cited by 3,075
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.Measure.restrictstatement and proof · cited by 1,646
- ENNReal.toRealstatement and proof · cited by 859
- MeasureTheory.Measure.realstatement and proof · cited by 530
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