Theorems · Theorem · sequences and series

Summable.tsum_le_of_sum_le

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : AddCommMonoid α] [inst_1 : Preorder α]
  [inst_2 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α} {a₂ : α} [L.NeBot],
  Summable f L → (∀ (s : Finset ι), ∑ i ∈ s, f i ≤ a₂) → ∑'[L] (i : ι), f i ≤ a₂

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

8 results in Mathlib

Foundations

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

Assumes

AddCommMonoidPreorderTopologicalSpaceOrderClosedTopologySummationFilter.NeBot