Theorems · Theorem · real analysis

BoundedVariationOn.tendsto_leftLim

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] [CompleteSpace E]
  [inst_3 : TopologicalSpace α] [OrderTopology α] {f : α → E},
  BoundedVariationOn f Set.univ → ∀ (x : α), Filter.Tendsto f (nhdsWithin x (Set.Iio x)) (nhds (Function.leftLim f x))

A bounded variation function tends to its left-limit on its left.

Defined in

Mathlib.Topology.EMetricSpace.BoundedVariation

Cited by

5 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderPseudoEMetricSpaceCompleteSpaceTopologicalSpaceOrderTopology