Theorems · Theorem · measure theory
MeasureTheory.Measure.ae_mem_finset_iff
∀ {α : Type u_4} {mα : MeasurableSpace α} [MeasurableSingletonClass α] {μ : MeasureTheory.Measure α} {s : Finset α},
(∀ᵐ (a : α) ∂μ, a ∈ s) ↔ μ = ∑ a ∈ s, μ {a} • MeasureTheory.Measure.dirac a- Defined in
- Mathlib.MeasureTheory.Measure.Dirac
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSingletonClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
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
- Finsetstatement and proof · cited by 13,712
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidproof · cited by 12,281
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- SetLike.coeproof · cited by 8,199
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasurableSetproof · cited by 3,075
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.ae_mem_finset_iff_map_eq_sum_diracproof · cited by 1
- MeasureTheory.Measure.ae_eq_or_eq_iff_eq_dirac_add_diracproof · cited by 0