Theorems · Theorem · sequences and series

Multipliable.tprod_pow

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

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Basic

Cited by

3 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidTopologicalSpaceT2SpaceContinuousMulSummationFilter.NeBot