Theorems · Theorem · sequences and series

tprod_le_one

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : CommMonoid α] [inst_1 : Preorder α] [IsOrderedMonoid α]
  [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α}, (∀ (i : ι), f i ≤ 1) → ∏'[L] (i : ι), f i ≤ 1

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

CommMonoidPreorderIsOrderedMonoidTopologicalSpaceOrderClosedTopology