Theorems · Theorem · sequences and series

Multipliable.tprod_mul

∀ {α : Type u_1} {β : Type u_2} [inst : CommMonoid α] [inst_1 : TopologicalSpace α] {f g : β → α}
  {L : SummationFilter β} [T2Space α] [ContinuousMul α] [L.NeBot],
  Multipliable f L → Multipliable g L → ∏'[L] (b : β), f b * g b = (∏'[L] (b : β), f b) * ∏'[L] (b : β), g b

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommMonoidTopologicalSpaceT2SpaceContinuousMulSummationFilter.NeBot