Theorems · Theorem · functional analysis

SummableLocallyUniformlyOn_of_locally_bounded

∀ {α : Type u_1} {β : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup F] [CompleteSpace F]
  [inst_2 : TopologicalSpace β] [LocallyCompactSpace β] {f : α → β → F} {s : Set β},
  IsOpen s →
    (∀ K ⊆ s, IsCompact K → ∃ u, Summable u ∧ ∀ (n : α), ∀ k ∈ K, ‖f n k‖ ≤ u n) → SummableLocallyUniformlyOn f s

Defined in

Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn

Cited by

2 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupCompleteSpaceTopologicalSpaceLocallyCompactSpace