Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.eq_of_forall_toMeasure_apply_eq
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] (μ ν : MeasureTheory.FiniteMeasure Ω),
(∀ (s : Set Ω), MeasurableSet s → ↑μ s = ↑ν s) → μ = ν- Cited by
- 13 results in Mathlib
- Foundations
- Depth 171 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.
Cites9
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 · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.extproof · cited by 308
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- MeasureTheory.FiniteMeasure.toMeasurestatement and proof · cited by 87
Cited by13
Results whose statement or proof uses this declaration.
- isCompact_setOfPred_finiteMeasure_le_of_isCompactproof · cited by 2
- isCompact_setOfPred_probabilityMeasure_mass_eq_compl_isCompact_leproof · cited by 2
- MeasureTheory.FiniteMeasure.eq_of_forall_apply_eqproof · cited by 1
- MeasureTheory.FiniteMeasure.restrict_biUnion_finsetproof · cited by 1
- MeasureTheory.FiniteMeasure.restrict_unionproof · cited by 1
- MeasureTheory.FiniteMeasure.restrict_univproof · cited by 1
- MeasureTheory.FiniteMeasure.map_addproof · cited by 0
- MeasureTheory.FiniteMeasure.map_fst_prodproof · cited by 0
- MeasureTheory.FiniteMeasure.map_smulproof · cited by 0
- MeasureTheory.FiniteMeasure.eq_of_forall_toMeasure_apply_eq_iffproof · cited by 0
- MeasureTheory.FiniteMeasure.map_snd_prodproof · cited by 0
- MeasureTheory.ProbabilityMeasure.range_toFiniteMeasureproof · cited by 0