Theorems · Theorem · real analysis

BoundedVariationOn.tendsto_atTop_limUnder

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] [CompleteSpace E]
  [hE : Nonempty E] {f : α → E},
  BoundedVariationOn f Set.univ → Filter.Tendsto f Filter.atTop (nhds (Filter.atTop.limUnder f))

Defined in: Mathlib.Topology.EMetricSpace.BoundedVariation
Cited by: 1 results in Mathlib
Foundations: Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder PseudoEMetricSpace CompleteSpace Nonempty

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

LinearOrderstatement and proof · cited by 8,572
nhdsstatement and proof · cited by 5,554
Set.univstatement and proof · cited by 3,945
Filter.Tendstostatement and proof · cited by 3,814
CompleteSpacestatement and proof · cited by 2,532
Filter.atTopstatement and proof · cited by 2,405
PseudoEMetricSpacestatement and proof · cited by 1,536
inf_of_le_rightproof · cited by 128
BoundedVariationOnstatement and proof · cited by 65
Filter.limUnderstatement · cited by 47
Filter.principal_univproof · cited by 46
tendsto_nhds_limUnderproof · cited by 15

Cited by1

Results whose statement or proof uses this declaration.

BoundedVariationOn.vectorMeasure_Iciproof · cited by 2