Theorems · Theorem · number theory
Real.disjoint_residual_ae
Disjoint (residual ℝ) (MeasureTheory.ae MeasureTheory.volume)
The filters residual ℝ and ae volume are disjoint. This means that there exists a residual
set of Lebesgue measure zero (e.g., the set of Liouville numbers).
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- Foundations
- Depth 250 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- MeasureTheory.Measurestatement · cited by 10,939
- Filterstatement · cited by 8,121
- MeasureTheory.aestatement · cited by 2,352
- Disjointstatement · cited by 2,201
- MeasureTheory.MeasureSpace.volumestatement · cited by 1,323
- disjoint_compl_rightproof · cited by 47
- residualstatement · cited by 23
- Filter.disjoint_of_disjoint_of_memproof · cited by 15
- eventually_residual_liouvilleproof · cited by 2
- ae_not_liouvilleproof · cited by 2
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