Theorems · Theorem · real analysis
eVariationOn.eq_biSup_inter_Icc
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E} {s : Set α},
eVariationOn f s = ⨆ p ∈ {p | p.1 ∈ s ∧ p.2 ∈ s ∧ p.1 ≤ p.2}, eVariationOn f (s ∩ Set.Icc p.1 p.2)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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 and proof · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredstatement and proof · cited by 6,101
- iSupstatement and proof · cited by 2,415
- Finset.sum_congrproof · cited by 2,323
- le_antisymmproof · cited by 2,068
- Set.Iccstatement and proof · cited by 1,702
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Monotoneproof · cited by 1,397
- Finset.rangeproof · cited by 1,341
- Set.Iicproof · cited by 1,111
Cited by1
Results whose statement or proof uses this declaration.
- MonotoneOn.boundedVariationOnproof · cited by 0