Theorems · Theorem · measure theory
MeasureTheory.Measure.sum_smul_dirac
∀ {α : Type u_1} [inst : MeasurableSpace α] [Countable α] [MeasurableSingletonClass α] (μ : MeasureTheory.Measure α),
(MeasureTheory.Measure.sum fun a => μ {a} • MeasureTheory.Measure.dirac a) = μA measure on a countable type is a sum of Dirac measures.
- Defined in
- Mathlib.MeasureTheory.Measure.Dirac
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · cited by 62,936
- Setstatement · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Countablestatement and proof · cited by 633
- MeasurableSingletonClassstatement and proof · cited by 230
- MeasureTheory.Measure.diracstatement and proof · cited by 210
- MeasureTheory.Measure.sumstatement and proof · cited by 121
- measurable_idproof · cited by 89
- MeasureTheory.Measure.map_idproof · cited by 29
- MeasureTheory.Measure.map_eq_sumproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_countable'proof · cited by 4
- MeasureTheory.integral_countableproof · cited by 3
- MeasureTheory.Measure.tsum_indicator_apply_singletonproof · cited by 1