Theorems · Theorem · sequences and series

Multipliable.tprod_eq_mul_tprod_ite

∀ {α : Type u_1} {β : Type u_2} [inst : CommGroup α] [inst_1 : TopologicalSpace α] [IsTopologicalGroup α] {f : β → α}
  [T2Space α] [inst_4 : DecidableEq β],
  Multipliable f → ∀ (b : β), ∏' (n : β), f n = f b * ∏' (n : β), if n = b then 1 else f n

Let f : β → α be a multipliable function and let b ∈ β be an index. Lemma tprod_eq_mul_tprod_ite writes ∏ n, f n as f b times the product of the remaining terms.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Group

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommGroupTopologicalSpaceIsTopologicalGroupT2SpaceDecidableEq