Theorems · Theorem · sequences and series

tprod_nonneg

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : CommMonoidWithZero α] [inst_1 : TopologicalSpace α]
  [inst_2 : Preorder α] [ZeroLEOneClass α] [PosMulMono α] [ClosedIciTopology α] {f : ι → α},
  (∀ (i : ι), 0 ≤ f i) → 0 ≤ ∏'[L] (x : ι), f x

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

0 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidWithZeroTopologicalSpacePreorderZeroLEOneClassPosMulMonoClosedIciTopology