Theorems · Theorem · sequences and series

Summable.tsum_le_of_sum_range_le

∀ {α : Type u_3} [inst : Preorder α] [inst_1 : AddCommMonoid α] [inst_2 : TopologicalSpace α] {c : α}
  [ClosedIicTopology α] {f : ℕ → α}, Summable f → (∀ (n : ℕ), ∑ i ∈ Finset.range n, f i ≤ c) → ∑' (n : ℕ), f n ≤ c

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

3 results in Mathlib

Foundations

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

Assumes

PreorderAddCommMonoidTopologicalSpaceClosedIicTopology