Theorems · Theorem · functional analysis

HasSum.smul_const

∀ {ι : Type u_5} {R : Type u_7} {M : Type u_9} [inst : Semiring R] [inst_1 : TopologicalSpace R]
  [inst_2 : TopologicalSpace M] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [ContinuousSMul R M] {f : ι → R}
  {L : SummationFilter ι} {r : R}, HasSum f r L → ∀ (a : M), HasSum (fun z => f z • a) (r • a) L

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Module

Cited by

6 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceAddCommMonoidModuleContinuousSMul