Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.measurableSet_preimage
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] (f : MeasureTheory.SimpleFunc α β) (s : Set β),
MeasurableSet (⇑f ⁻¹' s)- Cited by
- 13 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- Set.preimagestatement · cited by 4,946
- MeasurableSetstatement · cited by 3,075
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- MeasurableSet.constproof · cited by 7
- MeasureTheory.SimpleFunc.measurableSet_cutproof · cited by 2
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.measurableproof · cited by 20
- MeasureTheory.SimpleFunc.inductionproof · cited by 14
- MeasureTheory.lintegral_eq_nnrealproof · cited by 6
- MeasureTheory.Measure.measurable_lintegralproof · cited by 3
- MeasureTheory.SimpleFunc.setToSimpleFunc_add_left'proof · cited by 2
- MeasureTheory.Measure.lintegral_joinproof · cited by 2
- MeasureTheory.SimpleFunc.lintegral_restrictproof · cited by 2
- MeasureTheory.SimpleFunc.induction'proof · cited by 1
- MeasureTheory.SimpleFunc.lintegral_map'proof · cited by 1
- MeasureTheory.SimpleFunc.lintegral_restrict_iUnion_of_directedproof · cited by 1
- MeasureTheory.SimpleFunc.lintegral_sumproof · cited by 1
- MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left'proof · cited by 1