Theorems · Theorem · measure theory
MeasureTheory.Measure.lintegral_rnDeriv_lt_top
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) [MeasureTheory.IsFiniteMeasure μ],
∫⁻ (x : α), μ.rnDeriv ν x ∂ν < ⊤- Cited by
- 9 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.
- 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
- Set.univproof · cited by 3,945
- MeasureTheory.lintegralstatement · cited by 1,152
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- LT.lt.neproof · cited by 872
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.measure_lt_topproof · cited by 39
- MeasureTheory.setLIntegral_univproof · cited by 23
- MeasureTheory.Measure.lintegral_rnDeriv_lt_top_of_measure_ne_topproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.integrable_rnDerivproof · cited by 9
- MeasureTheory.Measure.integrable_toReal_rnDerivproof · cited by 8
- MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eqproof · cited by 6
- MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eqproof · cited by 2
- MeasureTheory.Measure.rnDeriv_smul_leftproof · cited by 2
- MeasureTheory.Measure.rnDeriv_smul_rightproof · cited by 2
- MeasureTheory.rnDeriv_convproof · cited by 1
- MeasureTheory.Measure.rnDeriv_addproof · cited by 1
- MeasureTheory.rnDeriv_mconvproof · cited by 1