Theorems · Theorem · measure theory
Set.Infinite.meas_eq_top
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasurableSingletonClass α] {s : Set α},
s.Infinite → (∃ ε, ε ≠ 0 ∧ ∀ x ∈ s, ε ≤ μ {x}) → μ s = ⊤If all elements of an infinite set have measure uniformly separated from zero, then the set has infinite measure.
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- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSingletonClass
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Cites18
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 and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Set.Elemproof · cited by 7,166
- Infiniteproof · cited by 352
- Set.Infinitestatement and proof · cited by 263
- MeasurableSingletonClassstatement and proof · cited by 230
- Subtype.range_coe_subtypeproof · cited by 170
- top_uniqueproof · cited by 102
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