Theorems · Theorem · measure theory
MeasurableEmbedding.aemeasurable_comp_iff
∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} {m0 : MeasurableSpace α} [inst : MeasurableSpace β]
[inst_1 : MeasurableSpace γ] {f : α → β} {g : β → γ},
MeasurableEmbedding g → ∀ {μ : MeasureTheory.Measure α}, AEMeasurable (g ∘ f) μ ↔ AEMeasurable f μ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- AEMeasurablestatement and proof · cited by 840
- MeasurableEmbeddingstatement and proof · cited by 170
- Measurable.comp_aemeasurableproof · cited by 99
- Set.rangeFactorizationproof · cited by 56
- MeasurableEmbedding.injectiveproof · cited by 35
- MeasurableEmbedding.measurableproof · cited by 29
- Set.rangeSplittingproof · cited by 23
- Function.RightInverse.comp_eq_idproof · cited by 9
- Set.rightInverse_rangeSplittingproof · cited by 4
- MeasurableEmbedding.measurable_rangeSplittingproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Topology.IsEmbedding.aestronglyMeasurable_comp_iffproof · cited by 6
- aemeasurable_smul_constproof · cited by 0