Theorems · Theorem · sequences and series

Summable.abs

∀ {ι : Type u_1} {α : Type u_3} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α]
  [inst_3 : UniformSpace α] [IsUniformAddGroup α] [CompleteSpace α] {f : ι → α}, Summable f → Summable fun x => |f x|

Alias of the reverse direction of summable_abs_iff.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

5 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidUniformSpaceIsUniformAddGroupCompleteSpace