Theorems · Theorem · measure theory
MeasureTheory.SimpleFunc.sum_measure_preimage_singleton
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] (f : MeasureTheory.SimpleFunc α β)
{μ : MeasureTheory.Measure α} (s : Finset β), ∑ y ∈ s, μ (⇑f ⁻¹' {y}) = μ (⇑f ⁻¹' ↑s)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 190 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.
Cites12
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 and proof · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- SetLike.coestatement · cited by 8,199
- Finset.sumstatement · cited by 5,195
- Set.preimagestatement · cited by 4,946
- MeasureTheory.SimpleFuncstatement and proof · cited by 411
- MeasureTheory.SimpleFunc.measurableSet_fiberproof · cited by 20
- MeasureTheory.sum_measure_preimage_singletonproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.map_lintegralproof · cited by 7
- MeasureTheory.SimpleFunc.sum_range_measure_preimage_singletonproof · cited by 1