Theorems · Theorem · measure theory
IsClosed.measure_eq_univ_iff_eq
∀ {X : Type u_1} [inst : TopologicalSpace X] {m : MeasurableSpace X} {μ : MeasureTheory.Measure X} [μ.IsOpenPosMeasure]
{F : Set X} [OpensMeasurableSpace X] [MeasureTheory.IsFiniteMeasure μ], IsClosed F → (μ F = μ Set.univ ↔ F = Set.univ)- Defined in
- Mathlib.MeasureTheory.Measure.OpenPos
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 196 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
- Set.univstatement and proof · cited by 3,945
- IsClosedstatement and proof · cited by 1,639
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- OpensMeasurableSpacestatement and proof · cited by 636
- MeasurableSet.nullMeasurableSetproof · cited by 155
- MeasureTheory.Measure.IsOpenPosMeasurestatement and proof · cited by 80
Cited by2
Results whose statement or proof uses this declaration.
- NormedAddCommGroup.exists_norm_nsmul_leproof · cited by 1
- IsClosed.measure_eq_one_iff_eq_univproof · cited by 0