Theorems · Theorem · measure theory
StieltjesFunction.outer_Ioc
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : TopologicalSpace R] (f : StieltjesFunction R) [OrderTopology R]
[CompactIccSpace R] [DenselyOrdered R] (a b : R), f.outer (Set.Ioc a b) = ENNReal.ofReal (↑f b - ↑f a)- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites87
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
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- NNRealproof · cited by 4,310
- LE.le.transproof · cited by 3,151
- Set.iUnionproof · cited by 2,483
- zero_addproof · cited by 2,366
- LT.lt.leproof · cited by 2,189
Cited by2
Results whose statement or proof uses this declaration.
- StieltjesFunction.measure_Iocproof · cited by 8
- StieltjesFunction.outer_trimproof · cited by 0