Theorems · Theorem · measure theory
MeasureTheory.Measure.integrable_toReal_rnDeriv
∀ {𝓧 : Type u_1} {m𝓧 : MeasurableSpace 𝓧} {μ ν : MeasureTheory.Measure 𝓧} [MeasureTheory.IsFiniteMeasure μ],
MeasureTheory.Integrable (fun x => (μ.rnDeriv ν x).toReal) ν- Cited by
- 8 results in Mathlib
- Foundations
- Depth 213 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.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Integrablestatement · cited by 1,367
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- LT.lt.neproof · cited by 872
- ENNReal.toRealstatement · cited by 859
- Measurable.aemeasurableproof · cited by 304
- MeasureTheory.Measure.rnDerivstatement · cited by 234
- MeasureTheory.Measure.measurable_rnDerivproof · cited by 75
- MeasureTheory.Measure.lintegral_rnDeriv_lt_topproof · cited by 9
- MeasureTheory.integrable_toReal_of_lintegral_ne_topproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- InformationTheory.integrable_klFun_rnDeriv_iffproof · cited by 5
- MeasureTheory.toReal_rnDeriv_mapproof · cited by 5
- ConvexOn.map_condExp_rnDeriv_leproof · cited by 3
- InformationTheory.integral_klFun_rnDerivproof · cited by 2
- ConvexOn.integrable_apply_rnDeriv_of_integrable_compProdproof · cited by 1
- ConvexOn.integrable_comp_rnDeriv_trimproof · cited by 1
- MeasureTheory.le_integral_rnDeriv_of_acproof · cited by 1
- ConvexOn.apply_rnDeriv_ae_le_integralproof · cited by 1