Theorems · Theorem · sequences and series

Summable.tsum_lt_tsum

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

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

5 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupPartialOrderIsOrderedAddMonoidTopologicalSpaceIsTopologicalAddGroupOrderClosedTopologySummationFilter.NeBotSummationFilter.LeAtTop