Theorems · Theorem · real analysis
eVariationOn.subsingleton
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] (f : α → E) {s : Set α},
s.Subsingleton → eVariationOn f s = 0- Cited by
- 22 results in Mathlib
- Foundations
- Depth 152 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
- Set.Subsingletonstatement and proof · cited by 276
- eVariationOnstatement · cited by 90
- Set.Subsingleton.imageproof · cited by 14
- eVariationOn.constant_onproof · cited by 1
Cited by22
Results whose statement or proof uses this declaration.
- MonotoneOn.eVariationOn_eqproof · cited by 4
- hasConstantSpeedOnWith_iff_orderedproof · cited by 3
- BoundedVariationOn.tendsto_eVariationOn_Ici_zero_of_filterproof · cited by 3
- BoundedVariationOn.tendsto_eVariationOn_Ico_zeroproof · cited by 3
- HasConstantSpeedOnWith.unionproof · cited by 2
- eVariationOn.sumproof · cited by 2
- eVariationOn.comp_inter_Icc_eq_of_monotoneOnproof · cited by 2
- AbsolutelyContinuousOnInterval.boundedVariationOnproof · cited by 2
- eVariationOn.eVariationOn_Ioc_eq_Icc_of_continuousWithinAt'proof · cited by 2
- BoundedVariationOn.tendsto_eVariationOn_Icc_zero_leftproof · cited by 1
- eVariationOn.exists_lt_eVariationOn_inter_Iccproof · cited by 1
- BoundedVariationOn.continuousWithinAt_variationOnFromTo_Iciproof · cited by 1