Theorems · Theorem · measure theory
IsCompact.exists_isOpen_lt_add
∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace α]
[μ.InnerRegularCompactLTTop] [MeasureTheory.IsLocallyFiniteMeasure μ] [R1Space α] [BorelSpace α] {K : Set α},
IsCompact K → ∀ {ε : ENNReal}, ε ≠ 0 → ∃ U, K ⊆ U ∧ IsOpen U ∧ μ U < μ K + ε- Defined in
- Mathlib.MeasureTheory.Measure.Regular
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 201 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
- IsOpenstatement · cited by 2,400
- BorelSpacestatement and proof · cited by 1,602
- IsCompactstatement and proof · cited by 1,282
- LT.lt.neproof · cited by 872
- MeasureTheory.IsLocallyFiniteMeasurestatement and proof · cited by 171
- R1Spacestatement and proof · cited by 125
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.eventually_nhds_one_measure_smul_sdiff_ltproof · cited by 3
- MeasureTheory.eventually_nhds_zero_measure_vadd_sdiff_ltproof · cited by 2
- MeasurableSet.exists_isOpen_symmDiff_ltproof · cited by 1