Theorems · Theorem · sequences and series

Summable.tsum_mul_right

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : NonUnitalNonAssocSemiring α]
  [inst_1 : TopologicalSpace α] [IsTopologicalSemiring α] {f : ι → α} [T2Space α] [L.NeBot] (a : α),
  Summable f L → ∑'[L] (i : ι), f i * a = (∑'[L] (i : ι), f i) * a

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Ring

Cited by

3 results in Mathlib

Foundations

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

Assumes

NonUnitalNonAssocSemiringTopologicalSpaceIsTopologicalSemiringT2SpaceSummationFilter.NeBot