Theorems · Theorem · real analysis
variationOnFromTo.monotoneOn
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E} {s : Set α},
LocallyBoundedVariationOn f s → ∀ {a : α}, a ∈ s → MonotoneOn (variationOnFromTo f s a) s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 and proof · cited by 25,697
- LinearOrderstatement and proof · cited by 8,572
- PseudoEMetricSpacestatement and proof · cited by 1,536
- MonotoneOnstatement · cited by 311
- le_add_of_nonneg_rightproof · cited by 69
- LocallyBoundedVariationOnstatement and proof · cited by 41
- variationOnFromTostatement and proof · cited by 33
- variationOnFromTo.addproof · cited by 10
- variationOnFromTo.nonneg_of_leproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- has_unit_speed_naturalParameterizationproof · cited by 0