Theorems · Theorem · measure theory
MeasureTheory.exists_measurable_superset
∀ {α : Type u_1} [inst : MeasurableSpace α] (μ : MeasureTheory.Measure α) (s : Set α),
∃ t, s ⊆ t ∧ MeasurableSet t ∧ μ t = μ sFor every set there exists a measurable superset of the same measure.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.toOuterMeasureproof · cited by 75
- MeasureTheory.OuterMeasure.exists_measurable_superset_eq_trimproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.measurableSet_toMeasurableproof · cited by 62
- MeasureTheory.measure_toMeasurableproof · cited by 53
- MeasureTheory.subset_toMeasurableproof · cited by 52
- MeasureTheory.exists_measurable_superset_of_nullproof · cited by 10
- MeasureTheory.measure_inter_add_sdiff₀proof · cited by 6
- MeasureTheory.toMeasurable_defstatement and proof · cited by 6
- MeasureTheory.Measure.zero_oneproof · cited by 5
- MeasureTheory.Measure.measure_toMeasurable_inter_of_coverproof · cited by 1
- MeasureTheory.Measure.measure_toMeasurable_inter_of_sumproof · cited by 1
- Besicovitch.exist_finset_disjoint_balls_large_measureproof · cited by 1