Theorems · Theorem · measure theory
MeasureTheory.innerRegularWRT_isCompact_isClosed_iff_innerRegularWRT_isCompact_closure
∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace α] [R1Space α],
μ.InnerRegularWRT (fun s => IsCompact s ∧ IsClosed s) IsClosed ↔ μ.InnerRegularWRT (IsCompact ∘ closure) IsClosed- Cited by
- 2 results in Mathlib
- Foundations
- Depth 171 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.coeproof · 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
- ENNRealproof · cited by 9,879
- IsClosedstatement and proof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- closurestatement and proof · cited by 1,254
- LT.lt.trans_leproof · cited by 678
- MeasureTheory.measure_monoproof · cited by 338
- subset_closureproof · cited by 309
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.innerRegularWRT_isCompact_isClosedproof · cited by 1
- MeasureTheory.innerRegularWRT_isCompact_isClosed_iffproof · cited by 0