Theorems · Theorem · functional analysis

Summable.tsum_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} [T2Space M] [L.NeBot],
  Summable f L → ∀ (a : M), ∑'[L] (z : ι), f z • a = (∑'[L] (z : ι), f z) • a

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Module

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringTopologicalSpaceTopologicalSpaceAddCommMonoidModuleContinuousSMulT2SpaceSummationFilter.NeBot