Theorems · Theorem · Lie groups
MeasureTheory.measure_pos_iff_nonempty_of_isAddLeftInvariant
∀ {G : Type u_1} [inst : MeasurableSpace G] [inst_1 : TopologicalSpace G] [BorelSpace G] {μ : MeasureTheory.Measure G}
[inst_3 : AddGroup G] [IsTopologicalAddGroup G] [μ.IsAddLeftInvariant] [μ.Regular],
μ ≠ 0 → ∀ {s : Set G}, IsOpen s → (0 < μ s ↔ s.Nonempty)- Defined in
- Mathlib.MeasureTheory.Group.Measure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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
- AddGroupstatement and proof · cited by 4,410
- Set.Nonemptystatement · cited by 2,627
- IsOpenstatement and proof · cited by 2,400
- BorelSpacestatement and proof · cited by 1,602
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- pos_iff_ne_zeroproof · cited by 180
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.