Theorems · Theorem · measure theory
MeasureTheory.Measure.nonempty_support
∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : MeasurableSpace X] {μ : MeasureTheory.Measure X}
[HereditarilyLindelofSpace X], μ ≠ 0 → μ.support.Nonempty- Defined in
- Mathlib.MeasureTheory.Measure.Support
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.Nonemptystatement · cited by 2,627
- MeasureTheory.Measure.supportstatement · cited by 41
- HereditarilyLindelofSpacestatement and proof · cited by 31
- Set.Nonempty.rightproof · cited by 5
- MeasureTheory.Measure.measure_univ_posproof · cited by 3
- MeasureTheory.Measure.nonempty_inter_support_of_posproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.nonempty_support_iffproof · cited by 1