Theorems · Theorem · measure theory
AEMeasurable.mono_ac
∀ {α : Type u_2} {β : Type u_3} {m0 : MeasurableSpace α} [inst : MeasurableSpace β] {f : α → β}
{μ ν : MeasureTheory.Measure α}, AEMeasurable f ν → μ.AbsolutelyContinuous ν → AEMeasurable f μ- Cited by
- 6 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.ofPredproof · cited by 6,101
- AEMeasurablestatement and proof · cited by 840
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- AEMeasurable.mkproof · cited by 75
- AEMeasurable.ae_eq_mkproof · cited by 65
- AEMeasurable.measurable_mkproof · cited by 62
- MeasureTheory.Measure.AbsolutelyContinuous.ae_leproof · cited by 26
Cited by6
Results whose statement or proof uses this declaration.
- AEMeasurable.mono_measureproof · cited by 10
- MeasureTheory.pdf.quasiMeasurePreserving_hasPDFproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_right_of_absolutelyContinuousproof · cited by 1
- MeasureTheory.map_withDensity_abs_det_fderiv_eq_addHaarproof · cited by 1
- ProbabilityTheory.mgf_le_of_mem_Icc_of_integral_eq_zeroproof · cited by 1
- MeasureTheory.pdf.lintegral_pdf_mulproof · cited by 0