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Theorems · Theorem · real analysis

eVariationOn.lowerSemicontinuous_uniformOn

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] (s : Set α),
  LowerSemicontinuous fun f => eVariationOn f s

The map (eVariationOn · s) is lower semicontinuous for uniform convergence on s.

Defined in
Mathlib.Topology.EMetricSpace.BoundedVariation
Cited by
0 results in Mathlib
Foundations
Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderPseudoEMetricSpace

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