Theorems · Theorem · sequences and series

Summable.tsum_le_tsum_of_inj

∀ {ι : Type u_1} {κ : Type u_2} {α : Type u_3} [inst : AddCommMonoid α] [inst_1 : Preorder α] [IsOrderedAddMonoid α]
  [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α} {g : κ → α} (e : ι → κ),
  Function.Injective e →
    (∀ c ∉ Set.range e, 0 ≤ g c) → (∀ (i : ι), f i ≤ g (e i)) → Summable f → Summable g → tsum f ≤ tsum g

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

5 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPreorderIsOrderedAddMonoidTopologicalSpaceOrderClosedTopology