Theorems · Theorem · sequences and series

Topology.IsInducing.summable_iff_tsum_comp_mem_range

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : AddCommMonoid α] [inst_1 : TopologicalSpace α]
  {L : SummationFilter β} [inst_2 : AddCommMonoid γ] [inst_3 : TopologicalSpace γ] [T2Space γ] {G : Type u_4}
  [inst_5 : FunLike G α γ] [AddMonoidHomClass G α γ] {g : G},
  Topology.IsInducing ⇑g → ∀ (f : β → α), Summable f L ↔ Summable (⇑g ∘ f) L ∧ ∑'[L] (i : β), g (f i) ∈ Set.range ⇑g

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidTopologicalSpaceAddCommMonoidTopologicalSpaceT2SpaceFunLikeAddMonoidHomClass