Theorems · Theorem · measure theory
StieltjesFunction.length_eq
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : TopologicalSpace R] (f : StieltjesFunction R) [Nonempty R]
(s : Set R), f.length s = ⨅ a, ⨅ b, ⨅ (_ : s \ botSet ⊆ Set.Ioc a b), ENNReal.ofReal (↑f b - ↑f a)- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- iInfstatement and proof · cited by 1,690
- Set.Iocstatement and proof · cited by 971
- ENNReal.ofRealstatement and proof · cited by 863
- iInf_congr_Propproof · cited by 218
- StieltjesFunction.toFunstatement and proof · cited by 120
- StieltjesFunctionstatement and proof · cited by 85
- botSetstatement and proof · cited by 16
Cited by7
Results whose statement or proof uses this declaration.
- StieltjesFunction.length_sdiff_botSetproof · cited by 3
- StieltjesFunction.length_emptyproof · cited by 3
- StieltjesFunction.outer_Iocproof · cited by 2
- StieltjesFunction.length_Iocproof · cited by 2
- StieltjesFunction.measurableSet_Ioiproof · cited by 1
- StieltjesFunction.length_monoproof · cited by 1
- StieltjesFunction.outer_trimproof · cited by 0