Theorems · Theorem · functional analysis

HasSum.const_smul

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : AddCommMonoid α]
  [inst_2 : DistribSMul γ α] [ContinuousConstSMul γ α] {f : β → α} {L : SummationFilter β} {a : α} (b : γ),
  HasSum f a L → HasSum (fun i => b • f i) (b • a) L

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Module

Cited by

11 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceAddCommMonoidDistribSMulContinuousConstSMul