Theorems · Theorem · measure theory
IsCompact.closure_subset_measurableSet
∀ {γ : Type u_3} [inst : TopologicalSpace γ] [inst_1 : MeasurableSpace γ] [BorelSpace γ] [R1Space γ] {K s : Set γ},
IsCompact K → MeasurableSet s → K ⊆ s → closure K ⊆ sIf K is a compact set in an R₁ space and s ⊇ K is a Borel measurable superset,
then s includes the closure of K as well.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Set.ofPredproof · cited by 6,101
- MeasurableSetstatement and proof · cited by 3,075
- BorelSpacestatement and proof · cited by 1,602
- IsCompactstatement and proof · cited by 1,282
- closurestatement · cited by 1,254
- Inseparableproof · cited by 160
- R1Spacestatement and proof · cited by 125
- Set.iUnion₂_subset_iffproof · cited by 12
- IsCompact.closure_eq_biUnion_inseparableproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- IsCompact.measure_closureproof · cited by 10
- MeasurableSet.exists_isCompact_isClosed_lt_addproof · cited by 1
- MeasureTheory.innerRegularWRT_isCompact_isClosed_measure_ne_top_of_groupproof · cited by 1