Theorems · Theorem · measure theory
MeasureTheory.Measure.setLIntegral_rnDeriv_le
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} (s : Set α),
∫⁻ (x : α) in s, μ.rnDeriv ν x ∂ν ≤ μ s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- LE.le.transproof · cited by 3,151
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.Measure.le_iff'proof · cited by 10
- MeasureTheory.Measure.withDensity_rnDeriv_leproof · cited by 9
- MeasureTheory.withDensity_apply_leproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_le_one_of_leproof · cited by 2
- MeasureTheory.Measure.integrableOn_toReal_rnDerivproof · cited by 1
- MeasureTheory.Measure.lintegral_rnDeriv_leproof · cited by 0