Theorems · Definition · measure theory
StieltjesFunction.length
{R : Type u_1} → [inst : LinearOrder R] → [inst_1 : TopologicalSpace R] → StieltjesFunction R → Set R → ENNRealLength of an interval. This is the largest monotone function which correctly measures all intervals.
- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- ENNRealstatement · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- iInfproof · cited by 1,690
- Set.Iocproof · cited by 971
- ENNReal.ofRealproof · cited by 863
- IsEmptyproof · cited by 759
- StieltjesFunction.toFunproof · cited by 120
- StieltjesFunctionstatement and proof · cited by 85
- botSetproof · cited by 16
Cited by13
Results whose statement or proof uses this declaration.
- StieltjesFunction.length_eqstatement · cited by 7
- StieltjesFunction.measure_singletonproof · cited by 6
- StieltjesFunction.outerproof · cited by 6
- StieltjesFunction.length_emptystatement · cited by 3
- StieltjesFunction.length_eq_of_isEmptystatement · cited by 3
- StieltjesFunction.length_sdiff_botSetstatement · cited by 3
- StieltjesFunction.outer_le_lengthstatement · cited by 3
- StieltjesFunction.length_Iocstatement · cited by 2
- StieltjesFunction.outer_Iocproof · cited by 2
- StieltjesFunction.length_monostatement · cited by 1
- StieltjesFunction.measurableSet_Ioiproof · cited by 1
- StieltjesFunction.length_diff_botSetstatement · cited by 0