Theorems · Theorem · real analysis

eVariationOn.lowerSemicontinuous_aux

∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {ι : Type u_3} {F : ι → α → E}
  {p : Filter ι} {f : α → E} {s : Set α},
  (∀ x ∈ s, Filter.Tendsto (fun i => F i x) p (nhds (f x))) →
    ∀ {v : ENNReal}, v < eVariationOn f s → ∀ᶠ (n : ι) in p, v < eVariationOn (F n) s

Defined in

Mathlib.Topology.EMetricSpace.BoundedVariation

Cited by

2 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderPseudoEMetricSpace