Theorems · Theorem · real analysis

BoundedVariationOn.continuousWithinAt_variationOnFromTo_rightLim_Ici

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E}
  [inst_2 : TopologicalSpace α] [OrderTopology α] [T3Space E] [CompleteSpace E],
  BoundedVariationOn f Set.univ →
    ∀ {a x : α}, ContinuousWithinAt (variationOnFromTo (Function.rightLim f) Set.univ a) (Set.Ici x) x

Defined in: Mathlib.Topology.EMetricSpace.VariationOnFromTo
Cited by: 0 results in Mathlib
Foundations: Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder PseudoEMetricSpace TopologicalSpace OrderTopology T3Space CompleteSpace

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Realstatement · cited by 25,697
TopologicalSpacestatement and proof · cited by 24,529
LinearOrderstatement and proof · cited by 8,572
Set.univstatement and proof · cited by 3,945
CompleteSpacestatement and proof · cited by 2,532
PseudoEMetricSpacestatement and proof · cited by 1,536
OrderTopologystatement and proof · cited by 1,355
Set.Icistatement · cited by 1,070
ContinuousWithinAtstatement · cited by 512
BoundedVariationOnstatement and proof · cited by 65
Function.rightLimstatement · cited by 52
T3Spacestatement and proof · cited by 51

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