Theorems · Theorem · measure theory
MeasurableEmbedding.measurableSet_image
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {mα : MeasurableSpace α} [inst : MeasurableSpace β] {f : α → β},
MeasurableEmbedding f → (MeasurableSet (f '' s) ↔ MeasurableSet s)- Cited by
- 18 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, 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.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- Set.imagestatement and proof · cited by 5,609
- MeasurableSetstatement and proof · cited by 3,075
- MeasurableEmbeddingstatement and proof · cited by 170
- MeasurableEmbedding.injectiveproof · cited by 35
- Function.Injective.preimage_imageproof · cited by 30
- MeasurableEmbedding.measurableproof · cited by 29
- MeasurableEmbedding.measurableSet_image'proof · cited by 15
Cited by18
Results whose statement or proof uses this declaration.
- MeasurableEmbedding.map_applyproof · cited by 16
- MeasurableEmbedding.compproof · cited by 7
- ProbabilityTheory.Kernel.comapRight_apply'proof · cited by 4
- ProbabilityTheory.eq_condKernel_of_measure_eq_compProdproof · cited by 3
- MeasurableEmbedding.measurable_rangeSplittingproof · cited by 3
- MeasurableEmbedding.variation_mapproof · cited by 3
- MeasurableEmbedding.prodMk_leftproof · cited by 2
- MeasureTheory.borel_eq_borel_of_leproof · cited by 2
- ProbabilityTheory.Kernel.comapRight_compProd_id_prodproof · cited by 1
- MeasurableEmbedding.comap_restrictproof · cited by 1
- ContinuousOn.measurableEmbeddingproof · cited by 1
- MeasurableEmbedding.measurableSet_preimageproof · cited by 0