Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.mem_range
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] {f : MeasureTheory.SimpleFunc α β} {b : β},
b ∈ f.range ↔ b ∈ Set.range ⇑f- Cited by
- 13 results in Mathlib
- Foundations
- Depth 68 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.
Cites9
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 · cited by 53,352
- Finsetstatement · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- Set.rangestatement · cited by 4,705
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- MeasureTheory.SimpleFunc.rangestatement · cited by 97
- Set.Finite.mem_toFinsetproof · cited by 74
- MeasureTheory.SimpleFunc.finite_rangeproof · cited by 8
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.map_lintegralproof · cited by 7
- MeasureTheory.SimpleFunc.map_setToSimpleFuncproof · cited by 6
- MeasureTheory.SimpleFunc.mem_range_selfproof · cited by 4
- MeasureTheory.SimpleFunc.integral_eq_sum_of_subsetproof · cited by 3
- MeasureTheory.SimpleFunc.lintegral_eq_of_subsetproof · cited by 3
- MeasureTheory.setToFun_of_le_map_of_stronglyMeasurableproof · cited by 2
- MeasureTheory.SimpleFunc.setToSimpleFunc_nonneg'proof · cited by 2
- MeasureTheory.SimpleFunc.setToSimpleFunc_congr'proof · cited by 1
- MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_of_subsetproof · cited by 1
- MeasureTheory.SimpleFunc.range_zeroproof · cited by 1
- MeasureTheory.SimpleFunc.mem_range_of_measure_ne_zeroproof · cited by 1
- MeasureTheory.SimpleFunc.preimage_eq_empty_iffproof · cited by 0