Theorems · Theorem · measure theory
MeasureTheory.Measure.OuterRegular.ext_isOpen
∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace α]
{ν : MeasureTheory.Measure α} [μ.OuterRegular] [ν.OuterRegular], (∀ (U : Set α), IsOpen U → μ U = ν U) → μ = νOuter regular measures are determined by values on open sets.
- Defined in
- Mathlib.MeasureTheory.Measure.Regular
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- IsOpenstatement and proof · cited by 2,400
- iInfproof · cited by 1,690
- MeasureTheory.Measure.extproof · cited by 308
- iInf_congr_Propproof · cited by 218
- InfSetproof · cited by 145
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.isAddLeftInvariant_eq_smul_of_regularproof · cited by 4
- MeasureTheory.Measure.ext_of_integral_eq_on_compactlySupportedproof · cited by 3
- MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_regularproof · cited by 3
- MeasureTheory.Measure.OuterRegular.ext_isOpen_isBoundedproof · cited by 0