Theorems · Definition · measure theory
MeasurableEmbedding.equivRange
{α : Type u_1} →
{β : Type u_2} →
[inst : MeasurableSpace α] →
[inst_1 : MeasurableSpace β] → {f : α → β} → MeasurableEmbedding f → α ≃ᵐ ↑(Set.range f)The domain of f is equivalent to its range as measurable spaces,
if f is a measurable embedding
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 23 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.
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- Set.univproof · cited by 3,945
- MeasurableEquivstatement · cited by 269
- MeasurableEmbeddingstatement and proof · cited by 170
- MeasurableEquiv.symmproof · cited by 155
- MeasurableEquiv.transproof · cited by 13
- MeasurableEquiv.Set.univproof · cited by 0
- MeasurableEmbedding.equivImageproof · cited by 0
- MeasurableEquiv.castproof · cited by 0
Cited by5
Results whose statement or proof uses this declaration.
- MeasurableEmbedding.invFunproof · cited by 3
- MeasurableEmbedding.equivRange_applystatement · cited by 1
- MeasurableEmbedding.equivRange_symm_apply_mkstatement and proof · cited by 1
- MeasurableEmbedding.measurable_invFunproof · cited by 1
- MeasurableEmbedding.equivRange.congr_simpstatement and proof · cited by 0