Theorems · Theorem · real analysis
eVariationOn.mono
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] (f : α → E) {s t : Set α},
t ⊆ s → eVariationOn f t ≤ eVariationOn f s- Cited by
- 5 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- ENNRealstatement · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Monotoneproof · cited by 1,397
- iSup_leproof · cited by 190
- eVariationOnstatement · cited by 90
- eVariationOn.sum_leproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- BoundedVariationOn.monoproof · cited by 3
- BoundedVariationOn.tendsto_eVariationOn_Ici_zero_of_filterproof · cited by 3
- eVariationOn.eq_biSup_inter_Iccproof · cited by 1
- hasConstantSpeedOnWith_zero_iffproof · cited by 0
- variationOnFromTo.abs_le_eVariationOnproof · cited by 0