Theorems · Theorem · sequences and series

tsum_mul_left

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

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Ring

Cited by

21 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionSemiringTopologicalSpaceIsTopologicalSemiringT2Space