Theorems · Definition · measure theory
Real.finiteSpanningSetsInIooRat
(μ : MeasureTheory.Measure ℝ) →
[MeasureTheory.IsLocallyFiniteMeasure μ] → μ.FiniteSpanningSetsIn (⋃ a, ⋃ b, ⋃ (_ : a < b), {Set.Ioo ↑a ↑b})The intervals (-(n + 1), (n + 1)) form a finite spanning set in the set of open intervals
with rational endpoints for a locally finite measure μ on ℝ.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.iUnionstatement · cited by 2,483
- Set.Ioostatement and proof · cited by 1,214
- MeasureTheory.IsLocallyFiniteMeasurestatement and proof · cited by 171
- MeasureTheory.Measure.FiniteSpanningSetsInstatement · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.hausdorffMeasure_pi_realproof · cited by 3
- Real.measure_ext_Ioo_ratproof · cited by 2