Theorems · Theorem · measure theory
MeasureTheory.Measure.nonempty_support_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] [inst_1 : MeasurableSpace X] {μ : MeasureTheory.Measure X}
[HereditarilyLindelofSpace X], μ.support.Nonempty ↔ μ ≠ 0- Defined in
- Mathlib.MeasureTheory.Measure.Support
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 201 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 and proof · cited by 2,627
- Set.not_nonempty_iff_eq_emptyproof · cited by 56
- MeasureTheory.Measure.supportstatement and proof · cited by 41
- HereditarilyLindelofSpacestatement and proof · cited by 31
- MeasureTheory.Measure.nonempty_supportproof · cited by 1
- MeasureTheory.Measure.support_zeroproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.support_eq_empty_iffproof · cited by 1