Theorems · Theorem · functional analysis
Summable.mul_norm
∀ {R : Type u_1} {ι : Type u_2} {ι' : Type u_3} [inst : NormedRing R] {f : ι → R} {g : ι' → R},
(Summable fun x => ‖f x‖) → (Summable fun x => ‖g x‖) → Summable fun x => ‖f x.1 * g x.2‖- Defined in
- Mathlib.Analysis.Normed.Ring.InfiniteSum
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- NormedRingstatement and proof · cited by 924
- Summablestatement and proof · cited by 778
- norm_nonnegproof · cited by 725
- Summable.of_nonneg_of_leproof · cited by 36
- norm_mul_leproof · cited by 31
- Summable.mul_of_nonnegproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- summable_mul_of_summable_normproof · cited by 5
- summable_mul_of_summable_norm'proof · cited by 3