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Theorems · Theorem · real analysis

BoundedVariationOn.mono

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E} {s : Set α},
  BoundedVariationOn f s → ∀ {t : Set α}, t ⊆ s → BoundedVariationOn f t
Defined in
Mathlib.Topology.EMetricSpace.BoundedVariation
Cited by
3 results in Mathlib
Foundations
Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderPseudoEMetricSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

BoundedVariationOn.locallyBoundedVariationOn · cited by 5BoundedVariationOn.locall…BoundedVariationOn.tendsto_eVariationOn_Ico_zero · cited by 3BoundedVariationOn.tendst…BoundedVariationOn.exists_tendsto_left · cited by 2BoundedVariationOn.exists…Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderPseudoEMetricSpace · cited by 1536PseudoEMetricSpacene_top_of_le_ne_top · cited by 68ne_top_of_le_ne_topBoundedVariationOn · cited by 65BoundedVariationOneVariationOn.mono · cited by 5eVariationOn.monoBoundedVariationOn.monoCITED BYCITES

Cites6

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Cited by3

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