Theorems · Theorem · real analysis
eVariationOn.eVariationOn_rightLim_le
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] [inst_2 : TopologicalSpace α]
[OrderTopology α] {f : α → E} {s : Set α}, IsOpen s → eVariationOn (Function.rightLim f) s ≤ eVariationOn f s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Filterproof · cited by 8,121
- IsOpenstatement and proof · cited by 2,400
- PseudoEMetricSpacestatement and proof · cited by 1,536
- OrderTopologystatement and proof · cited by 1,355
- nhdsWithin_le_nhdsproof · cited by 145
- eVariationOnstatement · cited by 90
- MapClusterPtproof · cited by 78
- Function.rightLimstatement and proof · cited by 52
Cited by1
Results whose statement or proof uses this declaration.
- BoundedVariationOn.rightLimproof · cited by 2