Theorems · Theorem · sequences and series

Summable.tsum_le_tsum

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : AddCommMonoid α] [inst_1 : Preorder α]
  [IsOrderedAddMonoid α] [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {f g : ι → α} [L.NeBot],
  (∀ (i : ι), f i ≤ g i) → Summable f L → Summable g L → ∑'[L] (i : ι), f i ≤ ∑'[L] (i : ι), g i

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

27 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPreorderIsOrderedAddMonoidTopologicalSpaceOrderClosedTopologySummationFilter.NeBot