Theorems · Theorem · real analysis
AbsolutelyContinuousOnInterval.mono
∀ {X : Type u_1} [inst : PseudoMetricSpace X] {f : ℝ → X} {a b c d : ℝ},
AbsolutelyContinuousOnInterval f a b → Set.uIcc c d ⊆ Set.uIcc a b → AbsolutelyContinuousOnInterval f c d- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- le_reflproof · cited by 2,061
- PseudoMetricSpacestatement and proof · cited by 1,550
- le_transproof · cited by 985
- Filter.principalproof · cited by 740
- Set.uIccstatement and proof · cited by 393
- Filter.map_monoproof · cited by 63
- inf_le_infproof · cited by 54
- AbsolutelyContinuousOnIntervalstatement and proof · cited by 31
- AbsolutelyContinuousOnInterval.disjWithinproof · cited by 15
- AbsolutelyContinuousOnInterval.totalLengthFilterproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- AbsolutelyContinuousOnInterval.const_of_ae_hasDerivAt_zeroproof · cited by 1