Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.sum_range_measure_preimage_singleton
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] (f : MeasureTheory.SimpleFunc α β)
(μ : MeasureTheory.Measure α), ∑ y ∈ f.range, μ (⇑f ⁻¹' {y}) = μ Set.univ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 191 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Finset.sumstatement · cited by 5,195
- Set.preimagestatement and proof · cited by 4,946
- Set.univstatement and proof · cited by 3,945
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- MeasureTheory.SimpleFunc.rangestatement and proof · cited by 97
- Set.preimage_rangeproof · cited by 38
- MeasureTheory.SimpleFunc.coe_rangeproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Convex.integral_memproof · cited by 1