Theorems · Theorem · measure theory
MeasureTheory.Content.outerMeasure_opens
∀ {G : Type w} [inst : TopologicalSpace G] (μ : MeasureTheory.Content G) [R1Space G] (U : TopologicalSpace.Opens G),
μ.outerMeasure ↑U = μ.innerContent U- Defined in
- Mathlib.MeasureTheory.Measure.Content
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceR1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement · cited by 9,879
- SetLike.coestatement · cited by 8,199
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- MeasureTheory.OuterMeasurestatement · cited by 287
- TopologicalSpace.Opens.is_open'proof · cited by 139
- R1Spacestatement and proof · cited by 125
- isOpen_iUnionproof · cited by 88
- MeasureTheory.Contentstatement and proof · cited by 60
- MeasureTheory.Content.outerMeasurestatement · cited by 24
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Content.outerMeasure_interior_compactsproof · cited by 1
- MeasureTheory.Content.outerMeasure_leproof · cited by 1
- MeasureTheory.Content.outerMeasure_of_isOpenproof · cited by 1
- MeasureTheory.Content.outerMeasure_pos_of_is_mul_left_invariantproof · cited by 0
- MeasureTheory.Content.outerMeasure_exists_compactproof · cited by 0
- MeasureTheory.Content.outerMeasure_pos_of_is_add_left_invariantproof · cited by 0