Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.preimage_eq_empty_iff
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] (f : MeasureTheory.SimpleFunc α β) (b : β),
⇑f ⁻¹' {b} = ∅ ↔ b ∉ f.range- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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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.preimagestatement · cited by 4,946
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- MeasureTheory.SimpleFunc.rangestatement · cited by 97
- MeasureTheory.SimpleFunc.mem_rangeproof · cited by 13
- Set.preimage_singleton_eq_emptyproof · cited by 5
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