Theorems · Theorem · measure theory
Set.exists_isOpen_le_add
∀ {α : Type u_1} [inst : MeasurableSpace α] [inst_1 : TopologicalSpace α] (A : Set α) (μ : MeasureTheory.Measure α)
[μ.OuterRegular] {ε : ENNReal}, ε ≠ 0 → ∃ U ⊇ A, IsOpen U ∧ μ U ≤ μ A + ε- Defined in
- Mathlib.MeasureTheory.Measure.Regular
- Cited by
- 3 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.
Cites16
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
- Top.topproof · cited by 9,680
- Set.univproof · cited by 3,945
- IsOpenstatement and proof · cited by 2,400
- LT.lt.leproof · cited by 2,189
- eq_or_neproof · cited by 1,117
- Set.subset_univproof · cited by 228
Cited by3
Results whose statement or proof uses this declaration.
- VitaliFamily.measure_le_of_frequently_leproof · cited by 5
- RealRMK.measure_le_of_isCompact_of_integralproof · cited by 1
- Besicovitch.exists_closedBall_covering_tsum_measure_leproof · cited by 1