Theorems · Theorem · measure theory
measurable_of_isOpen
∀ {γ : Type u_3} {δ : Type u_5} [inst : TopologicalSpace γ] [inst_1 : MeasurableSpace γ] [BorelSpace γ]
[inst_3 : MeasurableSpace δ] {f : δ → γ}, (∀ (s : Set γ), IsOpen s → MeasurableSet (f ⁻¹' s)) → Measurable f- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Set.preimagestatement and proof · cited by 4,946
- MeasurableSetstatement and proof · cited by 3,075
- IsOpenstatement and proof · cited by 2,400
- BorelSpacestatement and proof · cited by 1,602
- Measurablestatement and proof · cited by 1,499
- BorelSpace.measurable_eqproof · cited by 26
- measurable_generateFromproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- measurable_of_isClosedproof · cited by 4
- ContinuousOn.aemeasurableproof · cited by 4
- ContinuousOn.measurable_piecewiseproof · cited by 2