Theorems · Theorem · measure theory
IsClosed.ae_eq_univ_iff_eq
∀ {X : Type u_1} [inst : TopologicalSpace X] {m : MeasurableSpace X} {μ : MeasureTheory.Measure X} [μ.IsOpenPosMeasure]
{F : Set X}, IsClosed F → (F =ᵐ[μ] Set.univ ↔ F = Set.univ)- Defined in
- Mathlib.MeasureTheory.Measure.OpenPos
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Set.univstatement and proof · cited by 3,945
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- IsClosedstatement and proof · cited by 1,639
- IsClosed.isOpen_complproof · cited by 126
- Filter.EventuallyEq.reflproof · cited by 108
- MeasureTheory.Measure.IsOpenPosMeasurestatement and proof · cited by 80
- Set.compl_empty_iffproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- IsClosed.measure_eq_univ_iff_eqproof · cited by 2