Theorems · Theorem · measure theory
StieltjesFunction.length_mono
∀ {R : Type u_1} [inst : LinearOrder R] [inst_1 : TopologicalSpace R] (f : StieltjesFunction R) {s₁ s₂ : Set R},
s₁ ⊆ s₂ → f.length s₁ ≤ f.length s₂- Defined in
- Mathlib.MeasureTheory.Measure.Stieltjes
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 128 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.
Cites17
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
- le_reflproof · cited by 2,061
- Set.Iocproof · cited by 971
- IsEmptyproof · cited by 759
- le_imp_le_of_le_of_leproof · cited by 576
- isEmpty_or_nonemptyproof · cited by 269
- StieltjesFunctionstatement and proof · cited by 85
- iInf_monoproof · cited by 29
- sdiff_le_sdiffproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- StieltjesFunction.measurableSet_Ioiproof · cited by 1