Theorems · Theorem · measure theory
MeasureTheory.Measure.ext_of_singleton
∀ {α : Type u_1} [inst : MeasurableSpace α] [Countable α] {μ ν : MeasureTheory.Measure α},
(∀ (a : α), μ {a} = ν {a}) → μ = νTwo measures on a countable space are equal if they agree on singletons.
- Defined in
- Mathlib.MeasureTheory.Measure.Dirac
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpaceCountable
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 and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.extproof · cited by 2,266
- MeasureTheory.Measure.restrictproof · cited by 1,646
- Countablestatement and proof · cited by 633
- MeasureTheory.Measure.diracproof · cited by 210
- Set.countable_rangeproof · cited by 31
- MeasureTheory.Measure.restrict_singletonproof · cited by 12
- MeasureTheory.Measure.ext_of_sUnion_eq_univproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.binomial_eq_sum_diracproof · cited by 2
- MeasureTheory.Measure.ext_iff_singletonproof · cited by 1