Theorems · Theorem · measure theory
MeasureTheory.measure_eq_zero_iff_eq_empty_of_vaddInvariant
∀ (G : Type u) {α : Type w} {m : MeasurableSpace α} [inst : AddGroup G] [inst_1 : AddAction G α]
{μ : MeasureTheory.Measure α} [MeasureTheory.VAddInvariantMeasure G α μ] [inst_3 : TopologicalSpace α]
[ContinuousConstVAdd G α] [AddAction.IsMinimal G α] {U : Set α} [μ.Regular], μ ≠ 0 → IsOpen U → (μ U = 0 ↔ U = ∅)- Defined in
- Mathlib.MeasureTheory.Group.Action
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
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
- AddGroupstatement and proof · cited by 4,410
- IsOpenstatement and proof · cited by 2,400
- AddActionstatement and proof · cited by 820
- pos_iff_ne_zeroproof · cited by 180
- not_iff_notproof · cited by 159
- MeasureTheory.VAddInvariantMeasurestatement and proof · cited by 114
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