Theorems · Theorem · general topology
Measurable.measurableEmbedding
∀ {γ : Type u_3} {α : Type u_4} [inst : MeasurableSpace α] {f : γ → α} [MeasurableSpace.CountablySeparated α]
[inst_2 : MeasurableSpace γ] [StandardBorelSpace γ], Measurable f → Function.Injective f → MeasurableEmbedding fAn injective measurable function from a standard Borel space to a countably separated measurable space is a measurable embedding.
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- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasurableSetproof · cited by 3,075
- Measurablestatement and proof · cited by 1,499
- StandardBorelSpacestatement and proof · cited by 304
- Function.Injective.injOnproof · cited by 280
- MeasurableEmbeddingstatement · cited by 170
- MeasurableSpace.CountablySeparatedstatement and proof · cited by 20
- MeasurableSet.image_of_measurable_injOnproof · cited by 1
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