Theorems · Theorem · measure theory
MeasureTheory.Measure.nonempty_inter_support_of_pos
∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : MeasurableSpace X] {μ : MeasureTheory.Measure X}
[HereditarilyLindelofSpace X] {s : Set X}, 0 < μ s → (s ∩ μ.support).Nonempty- Defined in
- Mathlib.MeasureTheory.Measure.Support
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 178 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 · cited by 9,879
- LE.le.transproof · cited by 3,151
- Set.Nonemptystatement · cited by 2,627
- Disjointproof · cited by 2,201
- MeasureTheory.Measure.toOuterMeasureproof · cited by 75
- MeasureTheory.Measure.supportstatement and proof · cited by 41
- MeasureTheory.OuterMeasure.monoproof · cited by 36
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.nonempty_supportproof · cited by 1