Theorems · Theorem · measure theory
MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_sdiff
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : MeasurableSpace α] (μ : MeasureTheory.Measure α) (s : Set α),
∃ u, IsOpen u ∧ μ.everywherePosSubset s = s \ uThe everywhere positive subset of a set is obtained by removing an open set.
- Cited by
- 4 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.
Cites21
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
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- LE.le.transproof · cited by 3,151
- IsOpenstatement and proof · cited by 2,400
- Set.extproof · cited by 2,266
- nhdsWithinproof · cited by 1,912
- IsOpen.mem_nhdsproof · cited by 470
Cited by4
Results whose statement or proof uses this declaration.
- IsCompact.everywherePosSubsetproof · cited by 2
- MeasurableSet.everywherePosSubsetproof · cited by 2
- IsClosed.everywherePosSubsetproof · cited by 2
- MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_diffproof · cited by 0