Theorems · Theorem · measure theory
MeasureTheory.Measure.QuasiMeasurePreserving.comp
∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
{mγ : MeasurableSpace γ} {μa : MeasureTheory.Measure α} {μb : MeasureTheory.Measure β} {μc : MeasureTheory.Measure γ}
{g : β → γ} {f : α → β},
MeasureTheory.Measure.QuasiMeasurePreserving g μb μc →
MeasureTheory.Measure.QuasiMeasurePreserving f μa μb → MeasureTheory.Measure.QuasiMeasurePreserving (g ∘ f) μa μc- Cited by
- 21 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- MeasureTheory.Measure.AbsolutelyContinuousproof · cited by 325
- Measurable.compproof · cited by 234
- MeasureTheory.Measure.QuasiMeasurePreservingstatement and proof · cited by 101
- MeasureTheory.Measure.map_mapproof · cited by 67
- MeasureTheory.Measure.QuasiMeasurePreserving.absolutelyContinuousproof · cited by 20
- MeasureTheory.Measure.AbsolutelyContinuous.transproof · cited by 17
- MeasureTheory.Measure.QuasiMeasurePreserving.measurableproof · cited by 12
- MeasureTheory.Measure.AbsolutelyContinuous.mapproof · cited by 11
Cited by21
Results whose statement or proof uses this declaration.
- MeasureTheory.QuasiMeasurePreserving.fstproof · cited by 11
- MeasureTheory.QuasiMeasurePreserving.sndproof · cited by 5
- MeasureTheory.QuasiMeasurePreserving.prod_of_leftproof · cited by 3
- MeasureTheory.quasiMeasurePreserving_inv_mulproof · cited by 3
- MeasureTheory.quasiMeasurePreserving_neg_addproof · cited by 3
- MeasureTheory.quasiMeasurePreserving_add_leftproof · cited by 1
- MeasureTheory.lconvolution_assoc₀proof · cited by 1
- MeasureTheory.mconv_withDensity_eq_mlconvolution₀proof · cited by 1
- MeasureTheory.quasiMeasurePreserving_div_leftproof · cited by 1
- MeasureTheory.mlconvolution_assoc₀proof · cited by 1
- MeasureTheory.conv_withDensity_eq_mlconvolution₀proof · cited by 1
- MeasureTheory.AEEqFun.compQuasiMeasurePreserving_compstatement and proof · cited by 1